Question: Information: - A shape is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material composition. - The Napoleonic Wars (1803-1815) were a series of major conflicts pitting the French Empire and its allies, led by Napoleon I, against a fluctuating array of European powers formed into various coalitions, primarily led and financed by the United Kingdom. The wars resulted from the unresolved disputes associated with the French Revolution and the Revolutionary Wars, which had raged on for years before concluding with the Treaty of Amiens in 1802. The resumption of hostilities the following year paved the way for more than a decade of constant warfare often categorized into five conflicts: the War of the Third Coalition (1805), the War of the Fourth Coalition (1806-7), the War of the Fifth Coalition (1809), the War of the Sixth Coalition (1813), and the War of the Seventh Coalition (1815). The Napoleonic Wars had profound consequences for global and European history, leading to the spread of nationalism and liberalism, the rise of the British Empire as the world's premier power, the independence movements in Latin America and the collapse of the Spanish Empire, the fundamental reorganization of German and Italian territories into larger states, and the establishment of radically new methods in warfare. - Emperor of the French (French: "Empereur des Francais") was the title used by the House of Bonaparte starting when Napoleon Bonaparte was given the title Emperor on 14 May 1804 by the French Senate and was crowned emperor of the French on 2 December 1804 at the cathedral of Notre Dame de Paris, in Paris with the Crown of Napoleon. - Napoleon Bonaparte ("Napoleon Bonaparte"; , born ""Napoleone di Buonaparte""; 15 August 1769 5 May 1821) was a French military and political leader who rose to prominence during the French Revolution and led several successful campaigns during the French Revolutionary Wars. As Napoleon I, he was Emperor of the French from 1804 until 1814, and again in 1815. Napoleon dominated European and global affairs for more than a decade while leading France against a series of coalitions in the Napoleonic Wars. He won most of these wars and the vast majority of his battles, building a large empire that ruled over continental Europe before its final collapse in 1815. One of the greatest commanders in history, his wars and campaigns are studied at military schools worldwide. Napoleon's political and cultural legacy has ensured his status as one of the most celebrated and controversial leaders in human history. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. - The French Revolutionary Wars were a series of sweeping military conflicts, lasting from 1792 until 1802, resulting from the French Revolution. They pitted the French First Republic against Britain, Austria and several other monarchies. They are divided in two periods: the War of the First Coalition (179297) and the War of the Second Coalition (17981802). Initially confined to Europe, the fighting gradually assumed a global dimension as the political ambitions of the Revolution expanded. After a decade of constant warfare and aggressive diplomacy, France had succeeded in seizing and conquering a wide array of territories, from the Italian Peninsula and the Low Countries in Europe to the Louisiana Territory in North America. French success in these conflicts ensured the spread of revolutionary principles over much of Europe. - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. - A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br> It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. - Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the "Elements". Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The "Elements" begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the "Elements" states results of what are now called algebra and number theory, explained in geometrical language. - The French Revolution was a period of far-reaching social and political upheaval in France that lasted from 1789 until 1799, and was partially carried forward by Napoleon during the later expansion of the French Empire. The Revolution overthrew the monarchy, established a republic, experienced violent periods of political turmoil, and finally culminated in a dictatorship under Napoleon that rapidly brought many of its principles to Western Europe and beyond. Inspired by liberal and radical ideas, the Revolution profoundly altered the course of modern history, triggering the global decline of absolute monarchies while replacing them with republics and liberal democracies. Through the Revolutionary Wars, it unleashed a wave of global conflicts that extended from the Caribbean to the Middle East. Historians widely regard the Revolution as one of the most important events in human history. - In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that curvature is not necessarily zero. - In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is the length of any of them. The name comes from Latin "r""adius", meaning "ray" but also the spoke of a chariot wheel. The plural of "radius" can be either "radii" (from the Latin plural) or the conventional English plural "radiuses". The typical abbreviation and mathematic variable name for "radius" is r. By extension, the diameter d is defined as twice the radius: - Lorenzo Mascheroni (May 13, 1750 July 14, 1800) was an Italian mathematician. - Napoleon 's problem is a famous compass construction problem . In it , a circle and its center are given . The challenge is to divide the circle into four equal arcs using only a compass . Napoleon was known to be an amateur mathematician but it is not known if he either created or solved the problem . Napoleon 's friend the Italian mathematician Lorenzo Mascheroni introduced the limitation of using only a compass ( no straight edge ) into geometric constructions . But actually , the challenge above is easier than the real Napoleon 's problem , consisting in finding the center of a given circle with compass alone . The following sections will describe solutions to both problems , and the proofs that they work . Georg Mohr 's 1672 book '' Euclides Danicus '' anticipated Mascheroni 's idea , though the book was only rediscovered in 1928 . What entity does 'napoleon's problem' has the relation 'instance of' with?
Answer:
mathematical problem