title: Royal Spanish Football Federation

text: On 21 May 1920, the General Assembly of the RFEF approved the creation of the national team to participate in the 1920 Antwerp Olympic Games. A committee of selectors made up of Paco Bru (representing the Catalonia region), José Angel Berraondo (from the North region) and Julián Ruete (from the Center region) was appointed, although the latter two ultimately resigned for personal reasons, and Luis Argüello (Treasurer of the Federation) joined the expedition.


title: Royal Spanish Football Federation

text: On 28 August 1920, the first official match of the Spanish national team was played, held at the La Butte stadium (now Joseph Marien Stadium) in Brussels, in front of some 3,000 spectators. Spain wore a red shirt, white shorts, black socks and an embroidered lion on the chest. The match ended with a 1-0 victory against Denmark, with a goal from Gipuzkoan Patricio Arabolaza in the 54th minute. In their maiden international tournament, Spain returned from Belgian lands with the silver medal after beating the Netherlands in the decisive match.


title: Royal Spanish Football Federation

text: On 30 June 1926 , after a long process, the clubs approved the first "Spanish Professional Football Regulations", thus, following the English model, the sport of football become professional in Spain. This would lay the foundation for the founding of the National League Championship (La Liga) in 1929.


title: Royal Spanish Football Federation

text: The first edition of La Liga ran from February to June 1929, and was played by ten clubs. Six clubs were selected for being Copa del Rey winners (Real Madrid, Barcelona, Athletic Bilbao, Arenas Club, Real Unión and Real Sociedad —as the successor club of the Club Ciclista), another three as runners-up (Atlético Madrid, RCD Espanyol and CE Europa), and to decide the tenth place, an eliminatory tournament between ten clubs was organized, which Racing de Santander won after beating Sevilla in the decisive match. Barcelona was proclaimed champion of the first league edition with 25 points, closely followed by Real Madrid at 23.


title: Royal Spanish Football Federation

text: The RFEF consists of 19 regional and territorial federations, comprising the different Autonomous communities and cities in Spain.


title: Beret

text: A beret ( or ; ; , ) is a soft, round, flat-crowned cap, usually of woven, hand-knitted wool, crocheted cotton, wool felt, or acrylic fibre.


title: Beret

text: Mass production of berets began in 19th century France and Spain, and the beret remains associated with these countries. Berets are worn as part of the uniform of many military and police units worldwide, as well as by other organizations.


title: Beret

text: Archaeology and art history indicate that headgear similar to the modern beret has been worn since the Bronze Age across Northern Europe and as far south as ancient Crete and Italy, where it was worn by the Minoans, Etruscans and Romans. Such headgear has been popular among the nobility and artists across Europe throughout modern history.


title: Beret

text: The Basque-style beret was the traditional headgear of Aragonese and Navarrian shepherds from the Ansó and Roncal valleys of the Pyrenees, a mountain range that divides southern France from northern Spain. The commercial production of Basque-style berets began in the 17th century in the Oloron-Sainte-Marie area of southern France. Originally a local craft, beret-making became industrialised in the 19th century. The first factory, Beatex-Laulhere, claims production records dating back to 1810. By the 1920s, berets were associated with the working classes in a part of France and Spain and by 1928 more than 20 French factories and some Spanish and Italian factories produced millions of berets.


title: Beret

text: In Western fashion, men and women have worn the beret since the 1920s as sportswear and later as a fashion statement.


title: Beret

text: Military berets were first adopted by the French Chasseurs Alpins in 1889. After seeing these during the First World War, British General Hugh Elles proposed the beret for use by the newly formed Royal Tank Regiment, which needed headgear that would stay on while climbing in and out of the small hatches of tanks. They were approved for use by King George V in 1924. Another possible origin of the RTR beret is that it was suggested to Alec Gatehouse by Eric Dorman-Smith. While the two officers were serving at Sandhurst in 1924, Gatehouse, who had transferred to the Royal Tank Corps, had been given the task of designing a practical headgear for the new corps. Dorman-Smith had toured Spain, including the Basque region, with his friend Ernest Hemingway during the past few years, and had acquired a black Basque beret during his travels.


title: Beret

text: The beret fits snugly around the head, and can be "shaped" in a variety of ways – in the Americas it is commonly worn pushed to one side. In Central and South America, local custom usually prescribes the manner of wearing the beret; there is no universal rule and older gentlemen usually wear it squared on the head, jutting forward. It can be worn by both men and women.


title: Beret

text: Military uniform berets feature a headband or sweatband attached to the wool, made either from leather, silk or cotton ribbon, sometimes with a drawstring allowing the wearer to tighten the cap. The drawstrings are, according to custom, either tied and cut off or tucked in or else left to dangle. The beret is often adorned with a cap badge, either in cloth or metal. Some berets have a piece of buckram or other stiffener in the position where the badge is intended to be worn.


title: Beret

text: Berets are not usually lined, but many are partially lined with silk or satin. In military berets, the headband is worn on the outside; military berets often have external sweatbands of leather, pleather or ribbon. The traditional beret (also worn by selected military units, such as the Belgian Chasseurs Ardennais or the French Chasseurs Alpins), usually has the "sweatband" folded inwardly. In such a case, these berets have only an additional inch or so of the same woollen material designed to be folded inwardly.


title: Beret

text: Berets came to be popularised across Europe and other parts of the world as typical Basque headgear, as reflected in their name in several languages (e.g. "béret basque" in French; "Baskenmütze" in German; "Basco" in Italian; "Tascu/Birritta" in Sicilian; or "baskeri" in Finnish), while the Basques themselves use the words "txapela" or "boneta". They are very popular and common in the Basque Country. The colours adopted for folk costumes varied by region and purpose: black and blue are worn more frequently than red and white, which are usually used at local festivities. The people of Aragon adopted red berets while the black beret became the common headgear of workers in France and Spain.


title: Beret

text: A big commemorative black beret is the usual trophy in sport or "bertso" competitions, including Basque rural sports, the Basque portions of the Tour de France, and the Vuelta Ciclista al Pais Vasco. It may bear sewn ornamental references to the achievement or contest.


title: Beret

text: The black beret was once considered the national cap of France in Anglo-Saxon countries and is part of the stereotypical image of the Onion Johnny. It is no longer as widely worn as it once was, but it remains a strong sign of local identity in the southwest of France. When French people want to picture themselves as "the typical average Frenchman" in France or in a foreign country, they often use this stereotype from Anglo-Saxon countries. There are today, three manufacturers in France. Laulhère (who acquired the formerly oldest manufacturer, Blancq-Olibet, in February 2014 ) has been making bérets since 1840. Manufacture de Bérets is a small artisan French beret manufacturer in the Béarnese town of Oloron-Sainte-Marie, and Le Béret Français is another artisan béret maker in the Béarnese village of Laàs. The beret still remains a strong symbol of the unique identity of southwestern France and is worn while celebrating traditional events.


title: Beret

text: In Spain, the beret is usually known as the "boina", sometimes also as "bilbaína" or "bilba". They were once common men's headwear in across the north and central areas of the country, in the regions of Castile (both north and south), Aragon, Navarre, Leonese, the Basque Country, Cantabria, Asturias, Extremadura and Galicia. The first areas to wear it were the Basque Country, Navarre and Castile, but it spread over most of Spain during the 19th century.


title: Beret

text: All over Spain it has ended up becoming a stereotype of rural people, often with negative connotations of boorishness and uncouthness, found in expressions such as ""paleto de boina a rosca"" ("a hick wearing a screwed-on boina"), which has reduced the number of boina wearers even more.


title: Beret

text: There are several Scottish variants of the beret, notably the "Scottish bonnet" or "Bluebonnet" (originally "bonaid" in Gaelic), whose ribbon cockade and feathers identify the wearer's clan and rank. Other Scottish types include the "tam-o'-shanter" (named after a Robert Burns' character in one of his poems) and the striped "Kilmarnock cap", both of which feature a large pompom in the centre.


title: Beret

text: Among a few well-known historic examples are the Scottish soldiers, who wore the blue bonnet in the 17th and 18th centuries, the Volontaires Cantabres, a French force raised in the Basque country in the 1740s to the 1760s, who also wore a blue beret, and the Carlist rebels, with their red berets, in 1830s Spain.


title: Beret

text: The French Chasseurs alpins, a corps of mountain troops created in 1888, were the first permanently established military force to wear the military beret as a standard headgear. As retained until the present day the chasseur beret is a large and somewhat floppy headdress.


title: Beret

text: In the 20th century, royal approval was given for the Royal Tank Corps to adopt the black beret in 1924, with the 11th Hussars adopting a brown beret in 1928. In World War II, the Royal Dragoons adopted the grey beret at the end of 1939, with other mechanised units of the British Army, such as the Royal Armoured Corps and the Guards Armoured Division, adopting the black beret in 1941. British officer Bernard Montgomery ("Monty") took to wearing a black beret given to him by the driver of his command vehicle in 1942, and it became his trademark.


title: Beret

text: The maroon beret (not to be confused with the red beret), was officially introduced in July 1942 at the direction of Major-General Frederick Browning, commander of the British 1st Airborne Division, and soon became an international symbol of airborne forces. In the 1950s the U.S. Army's newly conceived Special Forces units began to wear a green beret as headgear, following the custom of the British Royal Marines, which was officially adopted in 1961 with such units becoming known as the "Green Berets", and additional specialized forces in the Army, U.S. Air Force and other services also adopted berets as distinctive headgear.


title: Beret

text: The beret is part of the long-standing stereotype of the intellectual, film director, artist, "hipster", poet, bohemian and beatnik. The painter Rembrandt and the composer Richard Wagner, among others, wore berets. In the United States and Britain, the middle of the 20th century saw an explosion of berets in women's fashion. In the latter part of the 20th century, the beret was adopted by the Chinese both as a fashion statement and for its political undertones. Berets were also worn by bebop and jazz musicians like Dizzy Gillespie, Gene Krupa, Wardell Gray and Thelonious Monk.


title: Beret

text: "Guerrillero Heroico", an iconic photograph of the Argentine revolutionary Che Guevara, shows him wearing a black beret with a brass star.


title: Beret

text: In the 1960s several activist groups adopted the black beret. These include the Provisional Irish Republican Army (PIRA), the ETA (who wore black berets over hoods in public appearances), the Black Panther Party of the United States, formed in 1966, and the "Black Beret Cadre" (a similar Black Power organisation in Bermuda). In addition, the Brown Berets were a Chicano organisation formed in 1967.


title: Beret

text: The Young Lords Party, a Latino revolutionary organisation in the United States in the 1960s and 1970s, also wore berets, as did the Guardian Angels unarmed anti-crime citizen patrol units originated by Curtis Sliwa in New York City in the 1970s to patrol the streets and subways to discourage crime (red berets and matching shirts).


title: Beret

text: Adherents of the Rastafari movement often wear a very large knitted or crocheted black beret with red, gold and green circles atop their dreadlocks. The style is often erroneously called a "kufi", after the skullcap known as "kufune". They consider the beret and dreadlocks to be symbols of the biblical covenant of God with his chosen people, the "black Israelites". This style of hat is also known as a Rastacap.


title: Ilyushin Il-78

text: The Ilyushin Il-78 (; NATO reporting name Midas) is a Soviet/Russian four-engined aerial refueling tanker based on the Il-76 strategic airlifter.


title: Ilyushin Il-78

text: The Soviet Union's first dedicated tanker aircraft were variants of preexisting bombers, like the Tupolev Tu-16 and Myasishchev M-4. Their performance was deemed insufficient, especially so since new bomber models were slated to enter service (the Tupolev Tu-22M and the Tupolev Tu-160). In 1968, the development of a brand-new tanker started, taking the Ilyushin Il-76 as a basis. However, its performances were insufficient for use as a tanker: it could only transfer less than 10 tonnes of fuel to other aircraft. Instead of the basic Il-76, the improved Il-76MD version was chosen as the basis for the new tanker, named Il-78, thanks to its higher fuel capacity. The Il-78 tanker was developed and designed in the Ilyushin Aviation Complex in the Soviet Union. The Il-78 made its first flight on 26 June 1983, and it officially entered service in June 1987. Meanwhile, work on a version with a higher fuel capacity started. This version was called Il-78M, and it first flew on 7 March 1987. In total, 32 Il-78s, 13 Il-78Ms and a single Il-78E (a version exported to Libya) were built at the Tashkent Aviation Production Association, from 1984 to 1993.


title: Ilyushin Il-78

text: Taking the Il-76MD as its basis, the Il-78 airframe retains its general configuration. The tail turret is removed, and an air refuelling operator is situated in the rear gunner's position. Three aerial refueling pods are added: one under each wing, and one fixed to the rear fuselage. The basic Il-78 use three UPAZ-1 pods, while the Il-78M uses two UPAZ-1s under the wings, and one UPAZ-1M on the rear fuselage (the UPAZ-1M has a superior fuel transfer rate). The underwing pods are used to refuel tactical aircraft, while the fuselage one is used for heavier aircraft. The Il-78 uses the probe-and-drogue refueling method. The Il-78 can transfer fuel from its internal tanks, and two removable tanks located in the cargo hold. The Il-78M has three fixed tanks in its cargo hold. The basic Il-78 can transfer a maximum of 57.7 tonnes of fuel (internal tanks only) or 85.7 tonnes with the additional tanks, while the Il-78M can transfer 105.7 tonnes.


title: Winston Groom

text: Winston Francis Groom Jr. (March 23, 1943 – September 17, 2020) was an American novelist and non-fiction writer. He is best known for his novel "Forrest Gump" (1986), which became a cultural phenomenon after being adapted as a 1994 film of the same name, starring Tom Hanks. After the film was released, gaining a high box office and winning numerous awards, Groom's novel sold more than one million copies worldwide. Groom wrote a sequel, "Gump and Co.", published in 1995. His last novel was "El Paso" (2011).


title: Winston Groom

text: He also wrote a total of fifteen non-fiction works on such varied subjects as the American Civil War and World War I, including five multiple biographies.


title: Winston Groom

text: Groom was born in Washington, D.C., the son of Ruth (Knudsen), an English teacher, and Winston Francis Groom, a lawyer at the Pentagon. He and his family returned to Mobile, Alabama where the senior Groom practiced law.


title: Winston Groom

text: Winston Groom was raised in Mobile County, Alabama, where he attended the private University Military School (now known as UMS-Wright Preparatory School). His earliest ambition was to become a lawyer like his father. Groom attended the University of Alabama, where he became a member of Delta Tau Delta International Fraternity and the Army ROTC. While serving as a literary editor in college, he settled on a new ambition to become a writer. He graduated with Omicron Delta Kappa honors in 1965.


title: Winston Groom

text: Groom served in the United States Army from 1965 to 1967, including a tour of duty in the Vietnam War (from 66–67). Most of his service time was spent with the Fourth Infantry Division.


title: Winston Groom

text: Upon his return from Vietnam, Groom worked as a reporter for the "Washington Star", a Washington, D. C. newspaper covering the U.S. Department of Justice and U.S. federal courts. Groom resigned and moved to New York to pursue a career in writing novels. Groom's first novel was "Better Times Than These", published in 1978. "Better Times Than These" was about a rifle company in the Vietnam War whose patriotism and lives are shattered. According to P.J O'Rourke, journalist and political satirist, and a friend of Groom, "Better Times Than These" was "the best novel written about the Vietnam War."


title: Winston Groom

text: His next novel "As Summers Die" (1980) received better recognition. His book "Conversations with the Enemy" (1982) follows an American soldier who escapes from a POW camp in Vietnam and takes a plane back to the United States. Fourteen years later he is arrested for desertion. "Conversations with the Enemy" was a 1984 finalist for the Pulitzer Prize for General Non-Fiction.


title: Winston Groom

text: In 1985, Groom moved back to Mobile, Alabama, where he began to work on the novel "Forrest Gump". Years before, Groom's elderly father had told him about a mentally disabled boy he had known as a child. Groom began writing "Forrest Gump" the same day, and within six weeks finished the novel. "Forrest Gump" was published in 1986.


title: Winston Groom

text: Several years later, it was adapted by screenwriter Eric Roth as a 1994 film of the same name, starring Tom Hanks in the title role of Forrest Gump. The film received six Academy Awards and numerous others; its popularity propelled the novel to best-seller status, and it sold 1.7 million copies worldwide.


title: Winston Groom

text: Groom disputed accounting by Paramount Pictures related to profits from the film. He contended the company used Hollywood accounting to deflate profitability numbers; as a result, Groom received no payment, although he held a 3% profit share in it.


title: Winston Groom

text: In November 2011, Groom published his latest history, "Kearny's March: The Epic Creation of the American West, 1846–1847". Groom describes how Brigadier General Stephen W. Kearny's quest for westward adventure coincided with the expansionist desires of U.S. President James K. Polk. The book opens in mid-summer 1846, in the period of the Texas Annexation, the Mexican–American War, and brewing issues related to the American Civil War fifteen years in the future. Groom weaves into "Kearny's March" mountain man Kit Carson, Brigham Young and his Mormon followers, and members of the Donner party.


title: Winston Groom

text: At the time of his death in 2020, Groom was waiting for publication of "The Patriots", his biography of American leaders John Adams, Alexander Hamilton, and Thomas Jefferson.


title: Diophantine equation

text: In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one. An exponential Diophantine equation is one in which unknowns can appear in exponents.


title: Diophantine equation

text: Diophantine problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic curves, algebraic surfaces, or, more generally, algebraic sets, their study is a part of algebraic geometry that is called "Diophantine geometry".


title: Diophantine equation

text: The word "Diophantine" refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria, who made a study of such equations and was one of the first mathematicians to introduce symbolism into algebra. The mathematical study of Diophantine problems that Diophantus initiated is now called Diophantine analysis.


title: Diophantine equation

text: While individual equations present a kind of puzzle and have been considered throughout history, the formulation of general theories of Diophantine equations (beyond the case of linear and quadratic equations) was an achievement of the twentieth century.


title: Diophantine equation

text: In the following Diophantine equations, , , , and are the unknowns and the other letters are given constants:


title: Diophantine equation

text: The simplest linear Diophantine equation takes the form , where , and are given integers. The solutions are described by the following theorem:


title: Diophantine equation

text: Proof: If is this greatest common divisor, Bézout's identity asserts the existence of integers and such that . If is a multiple of , then for some integer , and is a solution. On the other hand, for every pair of integers and , the greatest common divisor of and divides . Thus, if the equation has a solution, then must be a multiple of . If and , then for every solution , we have


title: Diophantine equation

text: showing that is another solution. Finally, given two solutions such that , one deduces that . As and are coprime, Euclid's lemma shows that divides , and thus that there exists an integer such that and . Therefore, and , which completes the proof.


title: Diophantine equation

text: The Chinese remainder theorem describes an important class of linear Diophantine systems of equations: let be pairwise coprime integers greater than one, be arbitrary integers, and be the product . The Chinese remainder theorem asserts that the following linear Diophantine system has exactly one solution such that , and that the other solutions are obtained by adding to a multiple of :


title: Diophantine equation

text: More generally, every system of linear Diophantine equations may be solved by computing the Smith normal form of its matrix, in a way that is similar to the use of the reduced row echelon form to solve a system of linear equations over a field. Using matrix notation every system of linear Diophantine equations may be written


title: Diophantine equation

text: The computation of the Smith normal form of provides two unimodular matrices (that is matrices that are invertible over the integers and have ±1 as determinant) and of respective dimensions and , such that the matrix


title: Diophantine equation

text: is such that is not zero for not greater than some integer , and all the other entries are zero. The system to be solved may thus be rewritten as


title: Diophantine equation

text: This system is equivalent to the given one in the following sense: A column matrix of integers is a solution of the given system if and only if for some column matrix of integers such that .


title: Diophantine equation

text: It follows that the system has a solution if and only if divides for and for . If this condition is fulfilled, the solutions of the given system are


title: Diophantine equation

text: Hermite normal form may also be used for solving systems of linear Diophantine equations. However, Hermite normal form does not directly provide the solutions; to get the solutions from the Hermite normal form, one has to successively solve several linear equations. Nevertheless, Richard Zippel wrote that the Smith normal form "is somewhat more than is actually needed to solve linear diophantine equations. Instead of reducing the equation to diagonal form, we only need to make it triangular, which is called the Hermite normal form. The Hermite normal form is substantially easier to compute than the Smith normal form."


title: Diophantine equation

text: Integer linear programming amounts to finding some integer solutions (optimal in some sense) of linear systems that include also inequations. Thus systems of linear Diophantine equations are basic in this context, and textbooks on integer programming usually have a treatment of systems of linear Diophantine equations.


title: Diophantine equation

text: A homogeneous Diophantine equation is a Diophantine equation that is defined by a homogeneous polynomial. A typical such equation is the equation of Fermat's Last Theorem


title: Diophantine equation

text: As a homogeneous polynomial in indeterminates defines a hypersurface in the projective space of dimension , solving a homogeneous Diophantine equation is the same as finding the rational points of a projective hypersurface.


title: Diophantine equation

text: Solving a homogeneous Diophantine equation is generally a very difficult problem, even in the simplest non-trivial case of three indeterminates (in the case of two indeterminates the problem is equivalent with testing if a rational number is the th power of another rational number). A witness of the difficulty of the problem is Fermat's Last Theorem (for , there is no integer solution of the above equation), which needed more than three centuries of mathematicians' efforts before being solved.


title: Diophantine equation

text: For degrees higher than three, most known results are theorems asserting that there are no solutions (for example Fermat's Last Theorem) or that the number of solutions is finite (for example Falting's theorem).


title: Diophantine equation

text: For the degree three, there are general solving methods, which work on almost all equations that are encountered in practice, but no algorithm is known that works for every cubic equation.


title: Diophantine equation

text: Homogeneous Diophantine equations of degree two are easier to solve. The standard solving method proceeds in two steps. One has first to find one solution, or to prove that there is no solution. When a solution has been found, all solutions are then deduced.


title: Diophantine equation

text: For proving that there is no solution, one may reduce the equation modulo. For example, the Diophantine equation


title: Diophantine equation

text: does not have any other solution than the trivial solution . In fact, by dividing and by their greatest common divisor, one may suppose that they are coprime. The squares modulo 4 are congruent to 0 and 1. Thus the left-hand side of the equation is congruent to 0, 1, or 2, and the right-hand side is congruent to 0 or 3. Thus the equality may be obtained only if and are all even, and are thus not coprime. Thus the only solution is the trivial solution . This shows that there is no rational point on a circle of radius formula_5 centered at the origin.


title: Diophantine equation

text: More generally, the Hasse principle allows deciding whether a homogeneous Diophantine equation of degree two has an integer solution, and computing a solution if there exist.


title: Diophantine equation

text: If a non-trivial integer solution is known, one may produce all other solutions in the following way.


title: Diophantine equation

text: be a homogeneous Diophantine equation, where formula_7 is a quadratic form (that is, a homogeneous polynomial of degree 2), with integer coefficients. The "trivial solution" is the solution where all formula_8 are zero. If formula_9 is a non-trivial integer solution of this equation, then formula_10 are the homogeneous coordinates of a rational point of the hypersurface defined by . Conversely, if formula_11 are homogeneous coordinates of a rational point of this hypersurface, where formula_12 are integers, then formula_13 is an integer solution of the Diophantine equation. Moreover, the integer solutions that define a given rational point are all sequences of the form


title: Diophantine equation

text: It follows that solving the Diophantine equation formula_6 is completely reduced to finding the rational points of the corresponding projective hypersurface.


title: Diophantine equation

text: Let now formula_17 be an integer solution of the equation formula_18 As is a polynomial of degree two, a line passing through crosses the hypersurface at a single other point, which is rational if and only if the line is rational (that is, if the line is defined by rational parameters). This allows parameterizing the hypersurface by the lines passing through , and the rational points are the those that are obtained from rational lines, that is, those that correspond to rational values of the parameters.


title: Diophantine equation

text: By permuting the indices, one may suppose, without loss of generality that formula_19 Then one may pass to the affine case by considering the affine hypersurface defined by


title: Diophantine equation

text: If this rational point is a singular point, that is if all partial derivatives are zero at , all lines passing through are contained in the hypersurface, and one has a cone. The change of variables


title: Diophantine equation

text: does not change the rational points, and transforms into a homogeneous polynomial in variables. In this case, the problem may thus be solved by applying the method to an equation with fewer variables.


title: Diophantine equation

text: If the polynomial is a product of linear polynomials (possibly with non-rational coefficients), then it defines two hyperplanes. The intersection of these hyperplanes is a rational flat, and contains rational singular points. This case is thus a special instance of the preceding case.


title: Diophantine equation

text: Substituting this in , one gets a polynomial of degree two in formula_24 that is zero for formula_25 It is thus divisible by formula_26. The quotient is linear in formula_24 and may be solved for expressing formula_28 as a quotient of two polynomials of degree at most two in formula_29 with integer coefficients:


title: Diophantine equation

text: be the homogenization of formula_35 These quadratic polynomials with integer coefficients form a parameterization of the projective hypersurface defined by :


title: Diophantine equation

text: A point of the projective hypersurface defined by is rational if and only if it may be obtained from rational values of formula_37 As formula_38 are homogeneous polynomials, the point is not changed if all formula_39 are multiplied by the same rational number. Thus, one may suppose that formula_40 are coprime integers. It follows that the integer solutions of the Diophantine equation are exactly the sequences formula_41 where, for ,


title: Diophantine equation

text: where is an integer, formula_40 are coprime integers, and is the greatest common divisor of the integers formula_44


title: Diophantine equation

text: One could hope that the coprimality of the formula_39 could imply that . Unfortunately this is not the case, as shown in the next section.


title: Diophantine equation

text: is probably the first homogeneous Diophantine equation of degree two that has been studied. Its solutions are the Pythagorean triples. This is also the homogeneous equation of the unit circle. In this section, we show how the above method allows retrieving Euclid's formula for generating Pythagorean triples.


title: Diophantine equation

text: For retrieving exactly Euclid's formula, we start from the solution , corresponding to the point of the unit circle. A line passing through this point may be parameterized by its slope:


title: Diophantine equation

text: where is any integer, and are coprime integers, and is the greatest common divisor of the three numerators. In fact, if and are both odd, and if one is odd and the other is even.


title: Diophantine equation

text: This description of the solutions differs slightly from Euclid's formula because Euclid's formula considers only the solutions such that and are all positive, and does not distinguish between two triples that differ by the exchange of and ,


title: Diophantine equation

text: These traditional problems often lay unsolved for centuries, and mathematicians gradually came to understand their depth (in some cases), rather than treat them as puzzles.


title: Diophantine equation

text: The given information is that a father's age is 1 less than twice that of his son, and that the digits making up the father's age are reversed in the son's age (i.e. ). This leads to the equation , thus . Inspection gives the result , , and thus equals 73 years and equals 37 years. One may easily show that there is not any other solution with and positive integers less than 10.


title: Diophantine equation

text: Many well known puzzles in the field of recreational mathematics lead to diophantine equations. Examples include the cannonball problem, Archimedes's cattle problem and the monkey and the coconuts.


title: Diophantine equation

text: In 1637, Pierre de Fermat scribbled on the margin of his copy of "Arithmetica": "It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers." Stated in more modern language, "The equation has no solutions for any higher than 2." Following this, he wrote: "I have discovered a truly marvelous proof of this proposition, which this margin is too narrow to contain." Such a proof eluded mathematicians for centuries, however, and as such his statement became famous as Fermat's Last Theorem. It was not until 1995 that it was proven by the British mathematician Andrew Wiles.


title: Diophantine equation

text: In 1657, Fermat attempted to solve the Diophantine equation (solved by Brahmagupta over 1000 years earlier). The equation was eventually solved by Euler in the early 18th century, who also solved a number of other Diophantine equations. The smallest solution of this equation in positive integers is , (see Chakravala method).


title: Diophantine equation

text: In 1900, David Hilbert proposed the solvability of all Diophantine equations as the tenth of his fundamental problems. In 1970, Yuri Matiyasevich solved it negatively, building on work of Julia Robinson, Martin Davis, and Hilary Putnam to prove that a general algorithm for solving all Diophantine equations cannot exist.


title: Diophantine equation

text: Diophantine geometry, which is the application of techniques from algebraic geometry in this field, has continued to grow as a result; since treating arbitrary equations is a dead end, attention turns to equations that also have a geometric meaning. The central idea of Diophantine geometry is that of a rational point, namely a solution to a polynomial equation or a system of polynomial equations, which is a vector in a prescribed field , when is "not" algebraically closed.


title: Diophantine equation

text: One of the few general approaches is through the Hasse principle. Infinite descent is the traditional method, and has been pushed a long way.


title: Diophantine equation

text: The depth of the study of general Diophantine equations is shown by the characterisation of Diophantine sets as equivalently described as recursively enumerable. In other words, the general problem of Diophantine analysis is blessed or cursed with universality, and in any case is not something that will be solved except by re-expressing it in other terms.


title: Diophantine equation

text: The field of Diophantine approximation deals with the cases of "Diophantine inequalities". Here variables are still supposed to be integral, but some coefficients may be irrational numbers, and the equality sign is replaced by upper and lower bounds.


title: Diophantine equation

text: The single most celebrated question in the field, the conjecture known as Fermat's Last Theorem, was solved by Andrew Wiles, using tools from algebraic geometry developed during the last century rather than within number theory where the conjecture was originally formulated. Other major results, such as Faltings's theorem, have disposed of old conjectures.


title: Diophantine equation

text: If a Diophantine equation has as an additional variable or variables occurring as exponents, it is an exponential Diophantine equation. Examples include the Ramanujan–Nagell equation, , and the equation of the Fermat–Catalan conjecture and Beal's conjecture, with inequality restrictions on the exponents. A general theory for such equations is not available; particular cases such as Catalan's conjecture have been tackled. However, the majority are solved via ad hoc methods such as Størmer's theorem or even trial and error.


title: Al Weaver

text: Alexander Paul Weaver (born 3 January 1981) is an English actor and writer, best known for his role as curate Leonard Finch in the ITV series "Grantchester" (2014-present).


title: Al Weaver

text: Weaver was born in the Metropolitan Borough of Bolton in Greater Manchester, England. He went to Rivington and Blackrod High School and studied acting at the Guildhall School of Music and Drama.


title: Al Weaver

text: Weaver's first paid theatre role was in Trevor Nunn's 2004 production of "Hamlet", at the Old Vic theatre in London. Weaver played the Prince of Denmark on Monday evenings and at all matinees, whilst Ben Whishaw took on the role for evening performances, from Tuesday to Saturday.


title: Al Weaver

text: British politician Michael Portillo lauded Weaver's interpretation of Hamlet in "The New Statesman": "He [Weaver] gave meaning to the poetry, refusing to be rushed in the soliloquies or intimidated by them, varying volume and pace well. Frame by frame, he made credible Hamlet's progression from self-indulgence to nobility, so we could nearly believe Fortinbras' remark that 'he was likely, had he been put on,/To have proved most royally'."


title: Al Weaver

text: Weaver has appeared in minor roles in films such as "Colour Me Kubrick" (2005) (uncredited), "The Merchant of Venice" (2004), "Marie Antoinette" (2006), and "Unmade Beds" (2009); “Me and Orson Welles” (2009 film). he also played "The Kid" in "Doom", "Schwob" in "Colette", and an uncredited Gulf War soldier in "Armistice" (2014).


title: Al Weaver

text: His television credits include D.C. Billy Slaven in "The Inspector Lynley Mysteries" (episodes "In Pursuit of a Proper Sinner" and "A Cry for Justice") and National Antiquities Museum employee Andy Galbraith in "Sherlock" episode "The Blind Banker". Weaver has been in "Five Days" (TV miniseries) as Josh Fairley. He has also been in "Five Daughters" (TV miniseries) played Tom Alderton . Weaver also has been in "Secret State" as Josh Leyton. Weaver also appeared in "Southcliffe" (TV miniseries), where he played Anthony. Weaver was in "Life in Squares" (TV miniseries) and played Young Leonard Woolf. He was also in "The Smoke" where he played Tom. Weaver was in "The Nativity", in which he played Thomas. Weaver was in "Personal Affairs" playing Crawford Crawford.


title: Al Weaver

text: His theatre credits include Meshak in the Royal National Theatre's 2006-07 production of Helen Edmundson's "Coram Boy".


title: Al Weaver

text: Weaver plays fledgling Anglican curate Leonard Finch in the TV series "Grantchester" (since 2014), assisting the Vicar of Grantchester, Sidney Chambers, and later, Will Davenport.


title: Al Weaver

text: Radio credits include "", a 2017 biographical radio play by the English writer James Runcie. Weaver also presents radio shows at a pub called the Boogaloo based in north London. One is called Film And Telly Stuff, which he presents with actor Luke Neal and the other is called The Theme's Of Our Youth, which he presents with actor Jack Whitam.


title: Al Weaver

text: He is also known for his role as Rex in the game "Xenoblade Chronicles 2" released in December 2017. He reprised the role for the character's appearance in "Super Smash Bros. Ultimate", as well as the trailer revealing Pyra and Mythra as playable characters.


title: Al Weaver

text: In 2020, he stars in a choose-your-own-adventure sci-fi thriller video game "The Complex" as Dr. Rees Wakefield.


title: 2010 United States Senate elections

text: The 2010 United States Senate elections were held on November 2, 2010, from among the United States Senate's 100 seats. A special election was held on January 19, 2010, for a mid-term vacancy in Massachusetts. Thirty-four of the November elections were for six-year terms to the Senate's Class 3, while other three were special elections to finish incomplete terms. Those 37 November elections featured 19 incumbent Democrats (seven of whom retired or were defeated in the primary) and 18 incumbent Republicans (eight of whom retired or were defeated in the primary).


title: 2010 United States Senate elections

text: After the 2008 elections, the Senate was composed of 58 Democrats, 40 Republicans, and 2 independents who caucused with the Democrats. Despite losing the popular vote, Democrats retained control of the Senate after the election.


title: 2010 United States Senate elections

text: Republicans won four seats held by retiring Democrats and also defeated two incumbent Democrats, for a Republican net gain of six seats. This was the first time since 1994 that Republicans successfully defended all of their own seats. This was also the fourth consecutive election of Class 3 senators where Democrats failed to gain seats, and the third consecutive midterm election held in a president's first term where Republicans picked up seats. Despite the Republican gains, the Democrats retained a majority of the Senate with 51 seats plus the two independents who caucused with them, compared to the 47 Republican seats.


title: 2010 United States Senate elections

text: Shading indicates party with largest share of that line. Does not include the January 2010 special election in Massachusetts.


title: 2010 United States Senate elections

text: Of the seats with retiring Democrats, three seats were kept by Democrats, and three were won by Republicans.


title: 2010 United States Senate elections

text: Of the seats with Democratic incumbents running for re-election, eight Democrats were re-elected, one appointee was elected to finish her term, and one appointee was elected to the next full term. Two lost re-election. One lost renomination and his seat was subsequently won by a Republican.


title: 2010 United States Senate elections

text: Of the seats with Republicans incumbents running for re-election, eleven Republicans won re-election. One Republican lost renomination, but the seat was re-elected as a write-in.


title: 2010 United States Senate elections

text: In these special elections, the winner was seated in the fall of 2010 (excluding Massachusetts), once they qualified and their elections were certified. Sorted by election date, then state, then class.


title: 2010 United States Senate elections

text: In these regular elections, the winners were elected for the term beginning January 3, 2011; ordered by state.


title: 2010 United States Senate elections

text: Seven November races, as well as the Massachusetts special election in January, had margins less than 10%:


title: 2010 United States Senate elections

text: California was the tipping point state, where Barbara Boxer (D) defeated Carly Fiorina (R) by a margin of 10.0%.


title: 2010 United States Senate elections

text: Incumbent Republican Richard Shelby won re-election to a fifth term. On November 9, 1994, Shelby switched his party affiliation from Democratic to Republican, one day after the Republicans won control of both houses in the midterm elections, giving the Republicans a 53-47 majority in the Senate. He won his first full term as a Republican in 1998 by a large margin, and faced no significant opposition in 2004 and 2010.


title: 2010 United States Senate elections

text: Shelby had over $17 million in the bank, one of the highest of any candidate in the country. He had become even more popular in his opposition to the Troubled Asset Relief Program (TARP) and the Emergency Economic Stabilization Act of 2008, as the ranking member of the Senate Banking Committee.


title: 2010 United States Senate elections

text: The November general election in Alaska was preceded by primary elections which were held August 24, 2010. Scott McAdams, the Mayor of Sitka, became the Democratic nominee and Joe Miller, an attorney and former federal magistrate, became the Republican nominee after defeating incumbent Senator Lisa Murkowski in the Republican primary.


title: 2010 United States Senate elections

text: Murkowski garnered more than 100,000 write-in votes in the general election, many of which were challenged by Miller for various errors including minor misspellings. The appeal was denied Even if all the challenged votes were thrown out, Murkowski would have still had a lead of over 2,100 votes.


title: 2010 United States Senate elections

text: Incumbent Republican John McCain, who returned to the Senate after losing the presidency to Barack Obama in the 2008 presidential election, ran for re-election to a fifth term and won.


title: 2010 United States Senate elections

text: After spending over $20 million during the primaries, McCain still had more than $1million cash on hand after the primary election. Glassman criticized McCain on women's issues. In August 2010, Glassman released a TV advertisement called "Arizona First."


title: 2010 United States Senate elections

text: Incumbent Democrat Blanche Lincoln ran for re-election to a third term, but lost to Republican nominee John Boozman. Boozman became the first Republican in 138 years to win the seat. Arkansas had previously only elected one Republican senator since the Reconstruction, who was defeated after his first term in 2002 by Mark Pryor.


title: 2010 United States Senate elections

text: In 2009, Boxer was criticized for correcting a general who called her "ma'am". Brigadier General Michael Walsh was testifying on the Louisiana coastal restoration process in the wake of Hurricane Katrina and answered Boxer's query with "ma'am" when Boxer interrupted him. "Do me a favor," Boxer said. "can you say 'senator' instead of 'ma'am?'" "Yes, ma'am," Walsh interjected. "It's just a thing, I worked so hard to get that title, so I'd appreciate it. Thank you," she said. The Army's guide to protocol instructs service members to call members of the U.S. Senate "sir", "ma'am" or "senator". Fiorina used this incident prominently in campaign ads, as did David Zucker, who directed a humorous commercial for RightChange.com titled 'Call Me Senator.' In February 2010, Carly Fiorina put out a campaign ad attacking Republican rival Tom Campbell featuring a "demon sheep", creating international, mostly negative, publicity.


title: 2010 United States Senate elections

text: In December 2008, President-elect Barack Obama selected incumbent U.S. Senator Ken Salazar to become U.S. Secretary of the Interior. After Salazar resigned from his seat, Democratic Governor Bill Ritter appointed Denver Public Schools Superintendent Michael Bennet to fill the seat, who won re-election to his first full term.


title: 2010 United States Senate elections

text: This was one of the most expensive elections in the 2010 cycle, with more than $50 million spent total, including over $35 million in outside spending. Conservative third party groups hammered Bennet for voting 92% of the time with the Democratic leadership, including voting for healthcare reform and the stimulus package. Liberal third party groups called Buck extremist. Bennet focused on attacking Buck's views on abortion, which he believed should be banned including those of cases of rape and incest. He was also attacked for wanting to eliminate the 17th Amendment and refusing to prosecute an alleged rapist as Weld County district attorney. Planned Parenthood mounted a mail campaign, targeting women voters with the warning that "Colorado women can't trust Ken Buck." Bennet won the women vote by 17 points according to exit polls. After the election, Buck conceded to the Denver Post that the main reason why he lost is because of social issues.


title: 2010 United States Senate elections

text: Incumbent Democrat Christopher Dodd suffered from dropping approval ratings in the past few years due to major controversies, leading him to announce in January 2010 that he would retire, instead of seeking a sixth term. As Dodd was a Democrat, Richard Blumenthal, incumbent State Attorney General, announced on the same day that he would run for Dodd's seat. The Connecticut Democratic Party nominated Blumenthal on May 21. Businesswoman Linda McMahon won the state party's nominating convention and the August 10 Republican primary to become the Republican candidate.


title: 2010 United States Senate elections

text: This was a special election to fill Delaware's Class 2 Senate seat, then held by Ted Kaufman, an appointee. The seat had been previously held by long-time Senator Joe Biden, who vacated it when he became Vice President of the United States in 2009.


title: 2010 United States Senate elections

text: Incumbent Republican Senator Mel Martínez, who was elected in a very close race against Democrat Betty Castor with 49% of the vote in 2004, announced on December 2, 2008, that he would not run for re-election to a second term, then announcing on August 7, 2009, that he would resign prior to the end of his term. The Governor of Florida, Republican Charlie Crist, was required to appoint a successor and he chose his former Chief of Staff, George LeMieux. LeMieux, a placeholder who did not run in the election, replaced Martínez in the Senate on September 10, 2009.


title: 2010 United States Senate elections

text: Crist publicly announced he was running for the seat in mid-2009. When he declared his candidacy, he received many Republican endorsements, including the National Republican Senatorial Committee, Martínez, and 2008 Republican presidential nominee John McCain. However, his support of the American Recovery and Reinvestment Act of 2009 hurt his popularity among conservatives, and Tea Party candidate Marco Rubio, the former Speaker of the Florida House of Representatives, surged in the polls. In April 2010, Crist announced he would drop out of the Republican primary and run as an Independent. The National Republican Senatorial Committee withdrew its endorsement of Crist and demanded a refund of its campaign funds that it provided for the Crist campaign. Rubio went on to win the Republican primary against only token opposition.


title: 2010 United States Senate elections

text: Polling initially showed Crist neck and neck with Rubio, but by the end of August Rubio opened up a solid and consistent lead. He was supported by Republican and some Independent voters whereas Democratic and other Independents were split between Crist and Meek. Rubio went on to win the election with 49% of the vote to Crist's 30% and Meek's 20%.


title: 2010 United States Senate elections

text: Hawaii last elected a Republican Senator in 1970, and its current delegation to the United States Congress currently consists entirely of Democrats. Democrats have also won Hawaii's electoral votes in every presidential election since Ronald Reagan's landslide election in 1984. The exceptions at the time were then-Governor Linda Lingle (who was serving her second and final term) and then-U.S. Representative Charles Djou, both of whom were Republicans.


title: 2010 United States Senate elections

text: Sullivan, a heavy underdog, criticized Crapo for being in Washington for too long saying "Senator Crapo has been in Congress for 18 years. The country is struggling, and I think it's time to make a change." Crapo emphasized his conservative record in Washington.


title: 2010 United States Senate elections

text: Incumbent Democrat Roland Burris did not run in 2010. He suffered from poor approval ratings and was investigated by the Sangamon County, Illinois State's Attorney for perjury. Although no criminal charges were filed against him, he faced an investigation by the Senate Ethics Committee.


title: 2010 United States Senate elections

text: There were two ballot items for the same seat: a regular election, to fill the Class 3 seat beginning with the 112th United States Congress beginning on January 3, 2011, and a special election, to fill that seat for the final weeks of the 111th Congress, replacing the temporary appointment of Roland Burris to the vacancy created by Barack Obama's election to the presidency.


title: 2010 United States Senate elections

text: A federal court ruled that the candidates appearing on the ballot for the replacement election would be the ones of the regular election, and that the special election would appear after the regular election on the ballot.


title: 2010 United States Senate elections

text: Incumbent Democrat Evan Bayh decided in February 2010 to retire instead of seeking a third term shortly after former U.S. Senator Dan Coats announced his candidacy for Bayh's contested seat. No Democratic candidate submitted enough signatures by the deadline to run, leading Democratic officials to choose U.S. Congressman Brad Ellsworth to be the nominee. Coats won the election.


title: 2010 United States Senate elections

text: After Coats's win in the Republican primary, Ellsworth began to heavily criticize Coats for his ties to lobbyists. He called for more disclosure of the meetings lawmakers have with lobbyists, banning congressional staff from lobbying for six years after their congressional jobs, requiring Congress members to put all their investments in blind trusts, more disclosure of Senate candidates' personal financial information, and changes to the U.S. Senate filibuster rules. He proposed lowering number of votes required to break a filibuster to 55 from the current 60. In response to Ellsworth's charges, Coats published his lobbying record in an 815-page document.


title: 2010 United States Senate elections

text: Coats emphasized the individual issues rather than ethics reforms advocated by his opponent. He focused on Ellsworth's record of voting in support of the Economic Stimulus Act of 2008, cap-and-trade legislation, and health care bill. Coats opinion of the healthcare law was that "the only responsible solution ... is to repeal the Obama-Pelosi-Ellsworth health spending bill and quickly replace it with cost-effective, incremental pieces that will decrease costs, increase coverage and not break the bank."


title: 2010 United States Senate elections

text: Incumbent Chuck Grassley started the campaign moderately popular, but his approval ratings dropped somewhat during the campaign. However, the seat continued to be considered to be "Safe Republican" by many sources, with CQ Politics noting that Grassley is "one of Iowa's most durable politicians."


title: 2010 United States Senate elections

text: Conlin described herself as a "prairie progressive." She supported the recent landmark case of Varnum v. Brien, which legalized gay marriage in the state. She also supported repeal of "don't ask, don't tell."


title: 2010 United States Senate elections

text: Before the election, former political advisor John Maxwell claimed that Grassley would have his toughest race since his first U.S. Senate election in 1980, where he defeated incumbent John Culver with 53% of the vote. Grassley won all of his four re-election bids with nearly 70% of the vote against unknown opponents. Grassley won the election with 64.51% of the vote.


title: 2010 United States Senate elections

text: Incumbent Republican Sam Brownback retired to run for Governor of Kansas, instead of seeking a third term. Republican nominee Jerry Moran won the open seat. Kansas is one of the most Republican states in the nation; no Democrat has been elected to either Senate seat since 1932.


title: 2010 United States Senate elections

text: The retirement of Brownback, a popular U.S. Senator, led to a heavily competitive primary election. Tiahrt, who was on the Committee of Appropriations, had been accused of excessive earmarking while he was in Congress. From 2006 to 2008, Tiahrt had requested and supported a total of 63 solo earmarks, costing $53.9 million. In the same period, Moran had requested and supported a total of 29 earmarks, with a pricetag of $13.4 million.


title: 2010 United States Senate elections

text: After the primaries, Moran chose not to release any more negative advertisements. Democrat Lisa Johnston ran a low-profile, quiet race. On election day, she won only two counties: Wyandotte County and Douglas County, while Moran won statewide by a landslide.


title: 2010 United States Senate elections

text: Incumbent Republican Jim Bunning retired instead of seeking a third term. Republican nominee Rand Paul won the open seat.


title: 2010 United States Senate elections

text: On May 18, 2010, Paul won the Republican nomination. After conceding the election to Paul, Grayson said, "It's time to put all differences aside, unite behind Dr. Paul, he needs our help and I for one stand ready to serve".


title: 2010 United States Senate elections

text: Grayson attacked Paul for his "strange ideas," such as his opposition of the PATRIOT Act, and what Grayson alleged to be his support of closing down Guantanamo Bay and saying that Iran was not a threat. He also attacked Paul for being a Duke University fan. He sent out another TV ad and web video that stirred controversy by making the case that Paul believes that foreign policy decisions made prior to September 11, 2001, are partially to blame for the attacks. Paul immediately responded by launching a statewide television ad in which he expresses his "outrage at terrorists who killed 3,000 innocents" before accusing Grayson of a "lie" and a "shameful" tactic. Grayson accused the Fox News Channel of favoring Paul over him.


title: 2010 United States Senate elections

text: Conway began the race trailing Paul, but as he attacked his opponent's positions on social-welfare and criminal-justice policies, the polls began to tighten. The campaign attracted $8.5 million in contributions from outside groups, of which $6 million was spent to help Rand Paul and $2.5 million to help Conway. This money influx was in addition to the money spent by the candidates themselves: $6 million by Paul and $4.7 million by Conway.


title: 2010 United States Senate elections

text: Incumbent Republican David Vitter won re-election to a second term. Some speculated that Vitter's re-election might have become complicated, by the prostitution scandal revealed in 2007, but he continued to lead in aggregate polling against potential opponents.


title: 2010 United States Senate elections

text: Melançon heavily criticized Vitter for prostitution sex scandal. Vitter released television advertising criticizing Melancon for his support for Obama's stimulus package and his support for amnesty for illegal immigrants. Melancon claimed "In August, Melancon challenged Vitter to a series of five live, televised town hall-style debates across the state. In his 2004 campaign for Senate, Vitter committed to five live, televised debates. Since Melancon issued the challenge, Vitter and Melancon have been invited to a total of seven live, televised debates. Vitter only accepted invitations to debates hosted by WWL-TV and WDSU-TV, both in New Orleans."


title: 2010 United States Senate elections

text: Republican nominee Eric Wargotz, Queen Anne's County, Maryland Commission President and physician, compared Mikulski to a dinosaur by calling her a political "insidersaurus" for being in Washington for over thirty years An ad showed a hammer hitting a brick wall, breaking it down and citing criticisms of Mikulski's record as a U.S. Senator. Mikulski released advertisements emphasizing education and job creation. Despite Wargotz's limited campaign and resources he received the highest percentage of votes against Mikulski as an incumbent U.S. Senator


title: 2010 United States Senate elections

text: A special election was held January 19, 2010 to fill the Class 1 seat for the remainder of the term ending January 3, 2013. It was won by Republican Scott Brown.


title: 2010 United States Senate elections

text: Incumbent Democrat Ted Kennedy had died August 25, 2009. Governor of Massachusetts appointed Democrat Paul Kirk September 24, 2009 to continue the term pending this special election, in which Kirk was not a candidate.


title: 2010 United States Senate elections

text: The election was viewed by conservatives outside of Massachusetts as a referendum against President Barack Obama. But Brown stated that he didn't believe that it was a referendum on Obama. Although Democrats would retain control of both Houses of Congress until January 2011, Brown's victory greatly affected their political plans, most notably for the Patient Protection and Affordable Care Act, though the legislation was signed into law two months later. Brown became the first Republican to win this seat since the Democrats captured it in 1952, and as of 2022, this is the last Senate election in Massachusetts won by a Republican.


title: 2010 United States Senate elections

text: Incumbent Republican Kit Bond retired instead of seeking a fifth term. Republican nominee Roy Blunt won the open seat.


title: 2010 United States Senate elections

text: Democrat Robin Carnahan and national Democrats heavily criticized Blunt for his support of bailouts, calling him "Bailout Blunt." Blunt criticized her for supporting President Obama's stimulus package, the cap-and-trade energy bill, and the health care reform bill.


title: 2010 United States Senate elections

text: Reid was initially considered vulnerable, with the non-partisan Cook Political Report rating the election as a toss-up and the Rothenberg Political Report rating the state as toss-up. A June 9, 2010, Rasmussen Reports post-primary poll showed Angle leading incumbent Senator Harry Reid by a margin of 50% to 39%. However, a July 2010 poll showed Senator Reid leading Angle by 7 points, following nationwide attention to some of Angle's positions, as well as the endorsement of Reid by prominent Republicans. The change of margin, 18% in less than a month, is the largest in Senate elections history. On July 28, 2010, Rasmussen Reports moved the race from toss-up to leans Democratic. Later, it moved back to toss-up. Despite Angle leading by three points in the polls the days leading up to the election, Reid defeated her by 5.74%, even in her own county, Washoe County. Reid also secured huge numbers out of the Democratic stronghold of Clark County, which covers the Las Vegas Metropolitan Area.


title: 2010 United States Senate elections

text: Incumbent Republican Judd Gregg retired instead of seeking a fourth term. Republican nominee Kelly Ayotte won the open seat by over 23 points, after winning a close party primary. New Hampshire trended Democratic in the 2006 and 2008 elections, with Republican incumbents losing both of the state's House seats and its other Senate seat to Democrats, but polling conducted in late December 2008 showed Gregg defeating both of the state's U.S. Representatives in a hypothetical match-up.


title: 2010 United States Senate elections

text: Democrat Paul Hodes called himself a fiscal conservative, which was mocked by Republican Kelly Ayotte in a TV ad. Hodes was criticized for supporting President Obama's Economic Recovery package, a carbon energy tax, and Affordable Care Act. Hodes criticized Ayotte for numerous controversies. One ad was questioned Ayotte's honesty in dealing with the Lakes Region Ponzi scheme which defrauded investors of almost $80 million.


title: 2010 United States Senate elections

text: There were two elections, due to the resignation of Hillary Clinton in January 2009 to become the U.S. Secretary of State. Both senate races, along with the New York gubernatorial election, one with a vulnerable Democratic incumbent and the other an open race, respectively, was believed to lead major New York Republicans to gravitate towards them rather than challenge the popular Schumer. As it happened, however, New York Republicans had difficulty drawing top-tier candidates to any of the three races.


title: 2010 United States Senate elections

text: Governor David Paterson had appointed Democrat Kirsten Gillibrand to serve as United States Senator this special election, replacing former Senator Hillary Clinton, who resigned to serve as U.S. Secretary of State in the Barack Obama administration. The winner of the special election would complete the term ending in January 2013. Due to this special election, this was the first time since the ratification of the 17th Amendment in 1913 that all of New York's six statewide offices were up for popular election on the same date.


title: 2010 United States Senate elections

text: Gillibrand claimed to be an independent thinker and takes a back seat to no one. She also released television advertising touting her experience as from upstate New York. DioGuardi criticized Gillibrand's recent photos in Vogue magazine.


title: 2010 United States Senate elections

text: Incumbent Republican Richard Burr won re-election to a second term. Burr was the first incumbent to win re-election for this seat since Sam Ervin's last re-election in 1968. Burr's 54.8% also represented the highest vote share a North Carolina Republican received since the state began directly electing its senators.


title: 2010 United States Senate elections

text: This Senate seat was unfavorable to incumbents over the past several decades. No person elected to this seat was re-elected since Sam Ervin in 1968. His successor, Democrat Robert Burren Morgan, was defeated for re-election in 1980, along with many other incumbents from his party. His Republican successor, John Porter East, committed suicide in 1986. East's appointed successor, Jim Broyhill, served for just four months, resigning upon his November 1986 election loss to former Democratic Governor Terry Sanford. In 1992, the seat changed hands yet again, as Sanford was defeated by wealthy GOP businessman Lauch Faircloth, who himself lost in his bid for a second term six years later by John Edwards. In 2004, no incumbent was defeated, as Edwards was running for vice president and was not allowed to be on the ballot in both races. However, that year the seat did change parties for the fifth time in a row, with Richard Burr defeating Bill Clinton's onetime Chief of Staff Erskine Bowles.


title: 2010 United States Senate elections

text: Incumbent Democrat Byron Dorgan did not seek re-election. Republican Governor John Hoeven won the open seat. Incumbent Byron Dorgan never had a difficult time getting elected, as he obtained 59%, 63%, and 68% in his three senate election bids, respectively. However, in December 2009, Rasmussen Reports conducted a hypothetical matchup of Governor John Hoeven against the incumbent. Hoeven led by a large margin, 58% to Dorgan's 36%. 61% of the state still had a favorable view of Dorgan, and if pitted against State Senator Duane Sand, the incumbent led 52% to 37%.


title: 2010 United States Senate elections

text: Hoeven was challenged in the race by North Dakota State Senator Tracy Potter of Bismarck. Potter received the endorsement of the North Dakota Democratic-NPL Party at its state convention on March 27, 2010. Governor Hoeven and Senator Potter advanced to the November 2, 2010 general election following balloting in North Dakota's primary election, which was held June 8, 2010. Neither candidate faced any significant opposition in the primary election.


title: 2010 United States Senate elections

text: Incumbent Republican George Voinovich retired instead of seeking a third term. Republican former Director of the Office of Management and Budget, United States Trade Representative, and Congressman Rob Portman won the open seat.


title: 2010 United States Senate elections

text: Originally, the election was seen as a toss-up. His experience as a former Bush official was considered to be a big problem for Portman. Both President Barack Obama and Vice President Joe Biden campaigned for Fisher. Television advertisements were very negative. Fisher attacked Portman for helping to ship jobs overseas during his entire political career, backing deals that shipped jobs overseas, and the trade deficit with China, which grew by over $41 billion. Portman claimed in response that most jobs were being lost to other states, not countries. Portman attacked Fisher for supporting Obama's stimulus and cap and trade.


title: 2010 United States Senate elections

text: Winning the election, Portman received the majority of votes in 82 of 88 counties and in 15 of 18 Congressional districts, including the district of liberal U.S. Congressman Dennis Kucinich.


title: 2010 United States Senate elections

text: Incumbent first-term Republican Tom Coburn won re-election to a second term. Coburn, a very popular incumbent, promised to limit himself to two terms. Despite his popularity, he did release television advertisements. In 2009, Coburn's approval rating in a PPP poll was 59%, including a 39% approval rating among Democrats. His Democratic opponent is a perennial candidate who did little campaigning.


title: 2010 United States Senate elections

text: Incumbent Democrat Ron Wyden won re-election to a third full term. Wyden, a popular incumbent with a 52% approval rating in a July poll, touted bipartisanship and promised to hold town-hall meetings annually in each of Oregon's 36 counties and to open offices outside of Portland and Salem. A Survey USA poll taken a few days before the election showed that 23% of Republicans supported Wyden.


title: 2010 United States Senate elections

text: Huffman, widely considered as an underdog, financed his own campaign. He defended bonuses for Wall Street executives and questioned global warming.


title: 2010 United States Senate elections

text: Incumbent Republican-turned-Democrat Arlen Specter ran for re-election to a sixth term, but he lost in the Democratic primary to Joe Sestak. Republican nominee Pat Toomey then won the seat.


title: 2010 United States Senate elections

text: Incumbent Republican Jim DeMint won re-election to a second term. Alvin Greene, the Democratic nominee, was the first major-party African-American U.S. Senate candidate in South Carolina since Reconstruction. Alvin Greene's Democratic primary election win and his margin of victory surprised pundits. As of the primary, he had held no public campaign events, raised no money, and did not have a campaign website. A review of the primary election showed that of the state's 46 counties, half had a significant gap between the absentee and primary day ballots. For example, in Lancaster County, Vic Rawl won the absentees with 84 percent, while Greene won primary day by a double-digit margin. Rawl's campaign manager also claimed, "In only two of 88 precincts, do the number of votes Greene got plus the number we got equal the total cast."


title: 2010 United States Senate elections

text: Thune was narrowly elected to his first term over Democratic Senate Minority Leader Tom Daschle with 51% of the vote in 2004. In spite of his lack of seniority, Thune rose to the position of chairman of the Republican Policy Committee in the United States Senate.


title: 2010 United States Senate elections

text: No members of the South Dakota Democratic Party (or any other party) filed to challenge Thune. Scott Heidepriem, the South Dakota Senate Minority Leader and a Democratic candidate for Governor of South Dakota, said, "We just concluded that John Thune is an extremely popular senator who is going to win another term in the Senate."


title: 2010 United States Senate elections

text: Incumbent Republican Bob Bennett was seeking re-election to a fourth term, but was eliminated in the GOP state convention. Republican Mike Lee, who won the Republican primary, won the open seat.


title: 2010 United States Senate elections

text: At the Republican convention, incumbent Senator Bob Bennett finished third in balloting among delegates and was eliminated from the race. Business owner Tim Bridgewater finished first and attorney Mike Lee finished second, but Bridgewater did not receive enough votes to avoid a primary election runoff against Lee. At the Democratic convention, delegates nominated businessman Sam Granato, who received 77.5 percent of the vote.


title: 2010 United States Senate elections

text: Republican Dino Rossi heavily criticized Murray for her support of the 2009 economic stimulus package; however, Rossi's economic promises are nearly identical to those of President Bush who asked for the stimulus. Rossi supports repealing the Patient Protection and Affordable Care Act and the Dodd-Frank Wall Street Reform and Consumer Protection Act. He also criticized Murray for her support for earmarks. In response, Murray said, "You bet that seniority and leadership has a big thing to do with it, but the other part of it is, I get up every day and I work hard and I believe in this and I am going to continue fighting for the community I represent."


title: 2010 United States Senate elections

text: Long-time Democratic Senator Robert Byrd died June 28, 2010, and Democratic Governor Joe Manchin appointed Carte Goodwin to temporarily fill the vacancy. Goodwin pledged to not run for election to the seat in exchange for the appointment. Manchin won the open seat and served out the remainder of Byrd's elected term, which ended on January 3, 2013.


title: 2010 United States Senate elections

text: Incumbent Democrat Russ Feingold ran for re-election to a fourth term, but was defeated by political newcomer, Republican Ron Johnson. Johnson, a millionaire manufacturer and Tea Party movement favorite who was running for his first political office, was the front runner. In response to controversy over his ownership of stock in BP, Johnson said he would sell it when market conditions were favorable and possibly use the proceeds to help finance his Senate campaign. Feingold's first television ad was a positive ad released in March. In July 2010, Feingold's second 2010 television election ad attacked Johnson for alleged support for offshore drilling in the Great Lakes. Johnson quickly countered Feingold with a television ad of his own. Feingold's logo was "Moving Forward". In one ad he emphasized independence and called himself a "Penny Pincher." Johnson argued that his professions, manufacturer and accountant were underrepresented in the U.S. Senate, and there were too many lawyers (57 out of 100 members), including Feingold.


title: Franconia

text: Franconia (, ; Franconian dialect: "Franggn" ; ) is a region of Germany, characterised by its culture and Franconian dialect (German: "Fränkisch").


title: Franconia

text: The three administrative regions of Lower, Middle and Upper Franconia (largest cities, respectively: Würzburg, Nuremberg and Bamberg) in the State of Bavaria are part of the cultural region of Franconia, as are the adjacent Franconian-speaking South Thuringia, south of the Rennsteig ridge (largest city: Suhl), Heilbronn-Franconia (largest city: Schwäbisch Hall) in the state of Baden-Württemberg, and small parts of the state of Hesse.


title: Franconia

text: Those parts of the Vogtland lying in the state of Saxony (largest city: Plauen) are sometimes regarded as Franconian as well, because the Vogtlandian dialects are mostly East Franconian. The inhabitants of Saxon Vogtland, however, mostly do not consider themselves as Franconian. On the other hand, the inhabitants of the Hessian-speaking parts of Lower Franconia west of the Spessart mountains (largest city: Aschaffenburg) do consider themselves as Franconian. Heilbronn-Franconia's largest city of Heilbronn and its surrounding areas being South Franconian-speaking, those are only sometimes regarded as Franconian.


title: Franconia

text: Franconia's largest city and unofficial capital is Nuremberg, which is contiguous with Erlangen and Fürth, with which it forms a large conurbation, with around 1.3 million inhabitants.


title: Franconia

text: The German word "Franken"—Franconians—also refers to the ethnic group, which is mainly to be found in this region. They are to be distinguished from the Germanic tribe of the Franks, and historically formed their easternmost settlement area. The origins of Franconia lie in the settlement of the Franks from the 6th century in the area probably populated until then mainly by the Elbe Germanic people in the Main river area, known from the 9th century as East Francia ("Francia Orientalis"). In the Middle Ages the region formed much of the eastern part of the Duchy of Franconia and, from 1500, the Franconian Circle. The restructuring of the south German states by Napoleon, after the demise of the Holy Roman Empire, saw most of Franconia awarded to Bavaria.


title: Franconia

text: The German name for Franconia, "Franken", comes from the dative plural form of "Franke," a member of the Germanic tribe known as the Franks.


title: Franconia

text: The name of the Franks in turn derives from a word meaning "daring, bold", cognate with old Norwegian "frakkr", "quick, bold". Franks from the Middle and Lower Rhine gradually gained control of (and so gave their name to) what is now Franconia during the 6th to 8th centuries.


title: Franconia

text: English distinguishes between "Franks" (the early medieval Germanic people) and "Franconians" in reference to the high medieval stem duchy, following Middle Latin use of "Francia" for France vs. "Franconia" for the German duchy. In German the name "Franken" is equally used for both, while the French are called "Franzosen", after Old French "françois", from Latin "franciscus", from Late Latin "Francus", from "Frank", the Germanic tribe.


title: Franconia

text: The Franconian lands lie principally in Bavaria, north and south of the sinuous River Main which, together with the left (southern) Regnitz tributary, including its Rednitz and Pegnitz headstreams, drains most of Franconia. Other large rivers include the upper Werra in Thuringia and the Tauber, as well as the upper Jagst and Kocher streams in the west, both right tributaries of the Neckar. In southern Middle Franconia, the Altmühl flows towards the Danube; the Rhine–Main–Danube Canal crosses the European Watershed. The man-made Franconian Lake District has become a popular destination for day-trippers and tourists.


title: Franconia

text: The landscape is characterized by numerous "Mittelgebirge" ranges of the German Central Uplands. The Western natural border of Franconia is formed by the Spessart and Rhön Mountains, separating it from the former Rhenish Franconian lands around Aschaffenburg (officially part of Lower Franconia), whose inhabitants speak Hessian dialects. To the north rise the Rennsteig ridge of the Thuringian Forest, the Thuringian Highland and the Franconian Forest, the border with the Upper Saxon lands of Thuringia. The Franconian lands include the present-day South Thuringian districts of Schmalkalden-Meiningen, Hildburghausen and Sonneberg, the historical "Gau" of Grabfeld, held by the House of Henneberg from the 11th century and later part of the Wettin duchy of Saxe-Meiningen.


title: Franconia

text: In the east, the Fichtel Mountains lead to Vogtland, Bohemian Egerland ("Chebsko") in the Czech Republic, and the Bavarian Upper Palatinate. The hills of the Franconian Jura in the south mark the border with the Upper Bavarian region ("Altbayern"), historical Swabia, and the Danube basin. The northern parts of the Upper Bavarian Eichstätt District, territory of the historical Bishopric of Eichstätt, are also counted as part of Franconia.


title: Franconia

text: In the west, Franconia proper comprises the Tauber Franconia region along the Tauber river, which is largely part of the Main-Tauber-Kreis in Baden-Württemberg. The state's larger Heilbronn-Franken region also includes the adjacent Hohenlohe and Schwäbisch Hall districts. In the city of Heilbronn, beyond the Haller Ebene plateau, South Franconian dialects are spoken. Furthermore, in those easternmost parts of the Neckar-Odenwald-Kreis which had formerly belonged to the Bishopric of Würzburg, the inhabitants have preserved their Franconian identity. Franconian areas in East Hesse along Spessart and Rhön comprise Gersfeld and Ehrenberg.


title: Franconia

text: The two largest cities of Franconia are Nuremberg and Fürth. Though located on the southeastern periphery of the area, the Nuremberg metropolitan area is often identified as the economic and cultural centre of Franconia. Further cities in Bavarian Franconia include Fürth, Erlangen, Bayreuth, Bamberg, Aschaffenburg, Schweinfurt, Hof, Coburg, Ansbach and Schwabach. The major (East) Franconian towns in Baden-Württemberg are Schwäbisch Hall on the Kocher — the imperial city declared itself "Swabian" in 1442 — and Crailsheim on the Jagst river. The main towns in Thuringia are Suhl and Meiningen.


title: Franconia

text: Franconia may be distinguished from the regions that surround it by its peculiar historical factors and its cultural and especially linguistic characteristics, but it is not a political entity with a fixed or tightly defined area. As a result, it is debated whether some areas belong to Franconia or not. Pointers to a more precise definition of Franconia's boundaries include: the territories covered by the former Duchy of Franconia and former Franconian Circle, the range of the East Franconian dialect group, the common culture and history of the region and the use of the Franconian Rake on coats of arms, flags and seals. However, a sense of popular consciousness of being Franconian is only detectable from the 19th century onwards, which is why the circumstances of the emergence of a Frankish identity are disputed. Franconia has many cultural peculiarities which have been adopted from other regions and further developed.


title: Franconia

text: The following regions are counted as part of Franconia today: the Bavarian provinces of Lower Franconia, Upper Franconia and Middle Franconia, the municipality of Pyrbaum in the county of Neumarkt in der Oberpfalz, the northwestern part of the Upper Bavarian county of Eichstätt (covering the same area as the old county of Alt-Eichstätt), the East Franconian counties of South Thuringia, parts of Fulda and the Odenwaldkreis in Hesse, the Baden-Württemberg regions of Tauber Franconia and Hohenlohe as well as the region around the Badenian Buchen.


title: Franconia

text: In individual cases the membership of some areas is disputed. These include the Bavarian language area of Alt-Eichstätt and the Hessian-speaking region around Aschaffenburg, which was never part of the Franconian Imperial Circle. The affiliation of the city of Heilbronn, whose inhabitants do not call themselves Franks, is also controversial. Moreover, the sense of belonging to Franconia in the Frankish-speaking areas of Upper Palatinate, South Thuringia and Hesse is sometimes less marked.


title: Franconia

text: The region of Franconia is divided among the states of Hesse, Thuringia, Bavaria and Baden-Württemberg. The largest part of Franconia, both by population and area, belongs to the Free State of Bavaria and is divided into the three administrative regions ("Regierungsbezirke") of Middle Franconia (capital: Ansbach), Upper Franconia (capital: Bayreuth) and Lower Franconia (capital: Würzburg). The name of these regions, as in the case of Upper and Lower Bavaria, refers to their situation with respect to the river Main. Thus Upper Franconia lies on the upper reaches of the river, Lower Franconia on its lower reaches and Middle Franconia lies in between, although the Main itself does not flow through Middle Franconia. Where the boundaries of these three provinces meet (the 'tripoint') is the "Dreifrankenstein" ("Three Franconias Rock").


title: Franconia

text: The Franconian territories of Baden-Württemberg are the regions of Tauber Franconia and Hohenlohe (which belong to the Heilbronn-Franconia Region with its office in Heilbronn and form part of the Stuttgart Region) and the area around the Badenian Buchen in the Rhein-Neckar Region.


title: Franconia

text: The Franconian parts of Thuringia (Henneberg Franconia) lie within the Southwest Thuringia Planning Region.


title: Franconia

text: The Franconian regions in Hesse form the smaller parts of the districts of Fulda (Kassel region) and the Odenwaldkreis (Darmstadt region), or lie on the borders with Bavaria or Thuringia.


title: Franconia

text: The two most important rivers of the region are the Main and its primary tributary, the Regnitz. The tributaries of these two rivers in Franconia are the Tauber, Pegnitz, Rednitz and Franconian Saale. Other major rivers in the region are the Jagst and Kocher in Hohenlohe-Franconia, which empty into the Neckar north of Heilbronn in Baden-Württemberg, the Altmühl and the Wörnitz in Middle Franconia, both tributaries of the Danube, and the upper and middle reaches of the Werra, the right-hand headstream of the Weser. In the northeast of Upper Franconia rise two left-hand tributaries of the Elbe: the Saxon Saale and the Eger.


title: Franconia

text: The Main-Danube Canal connects the Main and Danube across Franconia, running from Bamberg via Nuremberg to Kelheim. It thus complements the Rhine, Main and Danube, helping to ensure a continuous navigable waterway between the North Sea and the Black Sea. In Franconia, there are only a few, often very small, natural lakes. This is due to fact that most natural lakes in Germany are glacial or volcanic in origin, and Franconia escaped both influences in recent earth history. Among the largest waterbodies are reservoirs, which are mostly used as water reserves for the relatively dry landscapes of Franconia. These includes the waters of the Franconian Lake District, which was established in the 1970s and is also a tourist attraction. The heart of these lakes is the Großer Brombachsee, which has an area of 8.7 km and is thus the largest waterbody in Franconia by surface area.


title: Franconia

text: Several Central Upland ranges dominate the Franconian countryside. In the southeast, Franconia is shielded from the rest of Bavaria by the Franconian Jura. In the east, the Fichtel Mountains form the border; in the north are Franconian Forest, the Thuringian Forest, the Rhön Mountains and the Spessart form a kind of natural barrier. To the west are the Franconian Heights and the Swabian-Franconian Forest. In the Franconian part of South Hesse is the Odenwald. Parts of the southern Thuringian Forest border on Franconia. The most important hill ranges in the interior of the region are the Steigerwald and the Franconian Jura with their sub-ranges of Hahnenkamm and Franconian Switzerland. The highest mountain in Franconia is the Schneeberg in the Fichtel Mountains which is . Other well-known mountains include the Ochsenkopf (1,024m), the Kreuzberg (927.8m) and the Hesselberg (689.4m). The outliers of the region include the Hesselberg and the Gleichberge. The lowest point in Franconia is the water level of the river Main in Kahl which lies at a height of 100 metres above sea level.


title: Franconia

text: In addition to the hill and mountain ranges, there are also several very level areas, including the Middle Franconian Basin and the Hohenlohe Plain. In the south of Franconia are smaller parts of the flat Nördlinger Ries, one of the best preserved impact craters on earth.


title: Franconia

text: Franconia's flora is dominated by deciduous and coniferous forests. Natural forests in Franconia occur mainly in the ranges of the Spessart, Franconian Forest, Odenwald and Steigerwald. The Nuremberg "Reichswald" is another great forest, located within the metropolitan region of Nuremberg. Other large areas of forest in the region are the Mönchswald, the Reichsforst in the Fichtel Mountains and the Selb Forest. In the river valleys along the Main and Tauber, the countryside was developed for viticulture. In Spessart there are great oak forests. Also widespread are calcareous grasslands, extensively used pastures on very oligotrophic, poor sites. In particular, the southern Franconian Jura, with the Altmühl Valley, is characterized by poor grassland of this type. Many of these places have been designated as a protected areas.


title: Franconia

text: Franconia has several regions with sandy habitats that are unique for south Germany and are protected as the so-called Sand Belt of Franconia or "Sandachse Franken". When the Altmühlsee reservoir was built, a bird island was created and designated as a nature reserve where a variety of birds nest. Another important reserve is the Black Moor in the Rhön, which is one of the most important bog areas in Central Europe. A well known reserve is the Luisenburg Rock Labyrinth at Wunsiedel, a felsenmeer of granite blocks up to several metres across. The establishment of the first Franconian national park in the Steigerwald caused controversy and its designation was rejected in July 2011 by the Bavarian government. The reason was the negative attitude of local population. Conservationists are now demanding protection for parts of the Steigerwald by nominating it for a World Heritage Site. There are several nature parks in Franconia, including the Altmühl Valley Nature Park, which, since 1969, has been one of the largest in Germany.


title: Franconia

text: Other nature parks are the Swabian-Franconian Forest Nature Park in Baden-Württemberg, and the nature parks of Bavarian Rhön, Fichtel Mountains, Franconian Heights, Franconian Forest, Franconian Switzerland-Franconian Jura, Haßberge, Spessart and Steigerwald in Bavaria, as well as the Bergstraße-Odenwald Nature Park which straddles Bavaria, Baden-Württemberg and Hesse. Nature parks cover almost half the area of Franconia.


title: Franconia

text: In 1991 UNESCO recognised the Rhön as a biosphere reserve. Among the most picturesque geotopes in Bavaria, are the Franconian sites of "Fossa Carolina", the Twelve Apostle Rocks ("Zwölf-Apostel-Felsen"), the Ehrenbürg, the cave ruins of Riesenburg and the lake of Frickenhäuser See. The European Bird Reserves in Franconia are found mainly in uplands like the Steigerwald, in large forests like Nuremberg's Imperial Forest or along rivers like the Altmühl. There are also numerous Special Areas of Conservation and protected landscapes. In Franconia there are very many tufas, raised stream beds near river sources within the karst landscape that are known as 'stone runnels' ("Steinerne Rinnen"). There are protected examples at Heidenheim and Wolfsbronn.


title: Franconia

text: Like large parts of Germany, Franconia only has a few large species of wild animal. Forest dwellers include various species of marten, fallow deer, red deer, roe deer, wild boar and fox. In natural areas such as the Fichtel mountains there are populations of lynx and capercaillie, and beaver and otter have grown in numbers. There are occasional sightings of animals that had long been extinct in Central Europe, for example, the wolf.


title: Franconia

text: Only in the extreme northeast of Franconia and in the Spessart are there Variscan outcrops of the crystalline basement, which were uplifted from below the surface when the Alps exerted a northwards-oriented pressure. These are rocks of pre-Permian vintage, which were folded during various stages of Variscan orogeny in the Late Palaeozoic - before about 380 to 300 million years ago - and, in places, were metamorphosed under high pressure and temperature or were crystallized by ascending magma in the Earth's crust. Rocks which were unchanged or only lightly metamorphosed, because they had been deformed at shallow crustal depths, include the Lower Carboniferous shale and greywacke of Franconian Forest. The Fichtel mountains, the Münchberg Plateau and the Spessart, by contrast, have more metamorphic rocks (phyllite, schist, amphibolite, gneiss). The Fichtel mountains are also characterized by large granite bodies, called post-kinematic plutons which, in the late phase of Variscan orogeny, intruded into the metamorphic rocks. In most cases these are S-type granites whose melting was caused by heated-up sedimentary rocks sunk deep into the Earth's crust. While the Fichtel and Franconian Forest can be assigned to the Saxo-Thuringian Zone of Central European Variscan orogeny, the Spessart belongs to the Central German Crystalline Zone. The Münchberg mass is variously attributed to the Saxo-Thuringian or Moldanubian Zones.


title: Franconia

text: A substantially larger part of the shallow subsurface in Franconia comprises Mesozoic, unmetamorphosed, unfolded rocks of the South German Scarplands. The regional geological element of the South German Scarplands is the Franconian Platform ("Süddeutsche Großscholle"). At the so-called Franconian Line, a significant fault line, the Saxo-Thuringian-Moldanubian basement was uplifted in places up to 2000 m above the Franconian Platform. The western two-thirds of Franconia is dominated by the Triassic with its sandstones, siltstones and claystones (so-called siliciclastics) of the bunter sandstone; the limestones and marls of the Muschelkalk and the mixed, but predominantly siliciclastic, sedimentary rocks of the Keuper. In the Rhön, the Triassic rocks are overlain and intruded by volcanic rock (basalts, basanites, phonolites and trachytes) of the Tertiary. The eastern third of Franconia is dominated by the Jurassic rocks of the Franconian Jura, with the dark shales of the Black Jura, the shales and ferruginous sandstones of the Brown Jura and, the weathering-resistant limestones and dolomitic rocks of the White Jura, which stand out from the landscape and form the actual ridge of the Franconian Jura itself. In the Jura, mostly siliciclastic sedimentary rocks formed in the Cretaceous have survived.


title: Franconia

text: The Mesozoic sediments have been deposited in largescale basin areas. During the Triassic, the Franconian part of these depressions was often part of the mainland, in the Jurassic it was covered for most of the time by a marginal sea of the western Tethys Ocean. At the time when the limestones and dolomites of the White Jura were being deposited, this sea was divided into sponge reefs and intervening lagoons. The reef bodies and the fine-grained lagoon limestones and marls are the material from which the majority of the Franconian Jura is composed today. Following a drop in the sea level towards the end of the Upper Jurassic, larger areas also became part of the mainland at the beginning of the subsequent Cretaceous period. During the Upper Cretaceous, the sea advanced again up to the area of the Franconian Jura. At the end of the Cretaceous, the sea then retreated again from the region. In addition, large parts of South and Central Germany experienced a general uplift -or in areas where the basement had broken through a substantial uplift - the course of formation of the Alps during the Tertiary. Since then, Franconia has been mainly influenced by erosion and weathering (especially in the Jura in the form of karst), which has ultimately led to formation of today's landscapes.


title: Franconia

text: The oldest macrofossils in Franconia, which are also the oldest in Bavaria, are archaeocyatha, sponge-like, goblet-shaped marine organisms, which were discovered in 2013 in a limestone block of Late Lower Cambrian age, about 520 million years old. The block comes from the vicinity Schwarzenbach am Wald from the so-called Heinersreuth Block Conglomerate ("Heinersreuther Blockkonglomerat"), a Lower Carboniferous wildflysch. However, the aforementioned archaeocyathids are not three-dimensional fossils, but two-dimensional thin sections. These thin sections had already been prepared and investigated in the 1970s but the archaeocyathids among them were apparently overlooked at that time.


title: Franconia

text: Better known and more highly respected fossil finds in Franconia come from the unfolded sedimentary rocks of the Triassic and Jurassic. The bunter sandstone, however, only has a relatively small number of preserved whole fossils. Much more commonly, it contains trace fossils, especially the tetrapod footprints of "Chirotherium". The type locality for these animal tracks is Hildburghausen in the Thuringian part of Franconia, where it occurs in the so-called Thuringian Chirotherium Sandstone ("Thüringer Chirotheriensandstein", main Middle Bunter Sandstone). "Chirotherium" is also found in the Bavarian and Württemberg parts of Franconia. Sites include Aura near Bad Kissingen, Karbach, Gambach and Külsheim. There the deposits are somewhat younger (Upper Bunter Sandstone), and the corresponding stratigraphic interval is called the Franconian Chirotherium Beds ("Fränkische Chirotherienschichten"). Among the less significant body fossil records of vertebrates are the procolophonid "Anomoiodon liliensterni" from Reurieth in the Thuringian part of Franconia and "Koiloskiosaurus coburgiensis" from Mittelberg near Coburg, both from the Thuringian Chirotherium Sandstone, and the Temnospondyle "Mastodonsaurus ingens" (possibly identical with the mastodonsaurus, "Heptasaurus cappelensis") from the Upper Bunter at Gambach.


title: Franconia

text: As early as the first decade of the 19th century George, Count of Münster began systematic fossil gathering and digs and in the Upper Muschelkalk at Bayreuth. For example, the Oschenberg hill near Laineck became the type locality of two relatively well-known marine reptiles of the Triassic period, later found in other parts of Central Europe: the "flat tooth lizard", "Placodus" and the "false lizard", "Nothosaurus".


title: Franconia

text: In Franconia's middle Keuper (the Feuerletten) is one of the best known and most common species of dinosaurs of Central Europe: "Plateosaurus engelhardti", an early representative of the sauropodomorpha. Its type locality is located at Heroldsberg south of Nuremberg. When the remains of "Plateosaurus" were first discovered there in 1834, it was the first discovery of a dinosaur on German soil, and this occurred even before the name "dinosauria" was coined. Another important "Plateosaurus" find in Franconia was made at Ellingen.