the-french-artist/wikipedia_20220301.simple_sentence_split huggingface dataset:
Honorary Doctor of Fine Arts from the University of Connecticut, and served as the commencement speaker, May 18, 1996. (
Honorary Doctor of Humane Letters degree from Swarthmore College, 1995. (
Honorary Doctor of Letters degree from California State Polytechnic University, Pomona, 1992. (
Honorary Doctor of Laws from the University of Pennsylvania, 1990.
He also served as the commencement speaker in May 1997.
Honorary Doctor of Letters degree from Brown University, May 1985. (
African American comedians
Criminals from Pennsylvania
African American players of American football
African-American military personnel
American football running backs
American musicians
Ham is meat that comes from a thigh of a pig.
Ham is a kind of pork, which is any meat from a pig.
Ham can be dry-cured or wet-cured.
Dry-cured ham is made by rubbing the meat with salt.
Then, it is dried and aged.
Wet-cured ham is made with brine.
Ham is pork.
Ham is one of the foods forbidden by kosher rules.
Types of dry-cured ham:
Prosciutto crudo (Italian)
Prosciutto di Parma (Italian)
Jambon de bayonne (French)
Jamón serrano (Spanish)
Jamón iberico (Spanish)
Country ham (American)
York ham (English)
Westphalian ham (German)
Spam is a canned meat food made by the Hormel Foods Corporation.
It is made from pork shoulder meat and ham.
Spam Lite, a newer kind of Spam, is made with pork and chicken.
There have been many ideas about what the word "Spam" means.
The Hormel Foods Corporation once said that it means "Shoulder of Pork and Ham", but in some dictionaries "Spam" means "spiced ham".
Spam was used a lot in World War II, as there wasn't proper meat.
Because of that, spam was used as a rationed item.
Jokes about Spam
The British comedy group Monty Python created a short play about Spam in 1970.
In it, a lady who does not like Spam is talking to a waitress in a restaurant when a bunch of Vikings cut their conversation by singing the word "Spam" over and over again.
The lady does not like what is happening and eventually the word "Spam" became widely used to mean unwanted email messages.
There is also a song called Spam.
It was sung by Weird Al Yankovic and first recorded in 1988.
A mushroom (also called a toadstool) is the part of a fungus that is like a fruit of a plant.
Unlike plants, mushrooms do not use sunlight to make energy for themselves.
Some mushrooms are edible (safe to be eaten), and are used for cooking in many countries, such as China, Korea and Europe.
Other mushrooms, however, are poisonous, and can kill people (or make them very sick) if they are eaten.
People who look for mushrooms to eat are called mycophagists, meaning "mushroom eater", while The act of looking for mushrooms is simply called "mushrooming".
Mushrooms helps to make a Healthy Bones and Good for Diabetics.
It is available in Different colours and Shapes.
Kinds of mushrooms
Agarics (includes very poisonous, and hallucinogenic kinds)
Boletus (edible)
Bracket fungi
Chanterelles (edible)
Coral fungi (edible)
Cup fungi (usually edible)
Jelly fungi (usually edible, but tastes bad)
Polypores (similar to boletes)
Psychedelic (also known as shrooms)
Puffballs (usually edible)
Stinkhorns (edible, but smells bad)
Tooth fungi
Structure of mushrooms
Most mushrooms have a stem and a cap.
The bottom of the cap sometimes has gills to hold spores, and sometimes holds the spores themselves.
Mushroom Expert
MykoWeb
An Aid to Mushroom Identification, Simon's Rock College
Online Edible Wild Mushroom Field Guide
Mushroom Observer (mushroomobserver.org), a collaborative mushroom recording and identification project
list of field guides to mushrooms , from the International Field Guides database
Research associations
Mushroom Mania; the Newsletter
North American Mycological Association
International Society for Mushroom Science
Pacific Northwest Fungi Online Journal
Factorization (also called factorisation and factoring) is taking a composite number apart into numbers that multiply together to get the original number.
These smaller numbers are called factors or divisors.
1 is a factor of all numbers.
Prime factorization is breaking apart a composite numbers into prime numbers that can be multiplied to give the larger number.
Note that since 1 is not prime, it is not included in the prime factorization.
For example, 12 can be factored as 4 × 3.
Since 4 is not a prime number, that is not its prime factorization.
12's prime factorization is in fact 3 × 2 × 2.
The numbers which are obtained from the factorization are usually ordered, for example, starting with the smallest number.
For example, 72=2^3*3^2.
The factorization of every number is unique.
This generalizes to:
Every number has a unique prime factorization
Every prime factorization corresponds to a unique number
Find two numbers that add up to 9 and can be multiplied to get 20.
Here, these numbers are 4 and 5.
A joint is the place where two or more bones make contact.
They allow movement (except for skull bones) and give mechanical support.
Joints have cartilage in between them, which help to make the movement flexible.
Joints are described structurally and functionally.
Structural classification is how the bones connect to each other; function is the degree of movement between the articulating bones.
Muhammad Hosni Said Mubarak (; 4 May 1928 – 25 February 2020), commonly known as Hosni Mubarak (), was an Egyptian politician.
He served as President of Egypt from 14 October 1981 to 11 February 2011.
Mubarak became the Vice-President of the Republic of Egypt after moving up the ranks of the Egyptian Air Force.
Then he became the President after President Anwar Sadat was assassinated on 6 October 1981.
His almost thirty-year presidency made him Egypt's longest-serving ruler since Muhammad Ali Pasha.
As President of Egypt, Mubarak is thought to have been one of the most powerful leaders in the region.
Under the 1971 Constitution of Egypt, Mubarak exercised strong control over the country and was generally considered a dictator.
In 2005, he called an election and easily won it.
Many opponents believed Mubarak changed the election results so he could win.
In early 2011, during the Arab Spring, there were huge protests against his government.
In the end, Mubarak resigned and handed over power to the armed forces.
It is hoped that elections later that year for a new government.
On 2 June 2012, Mubarak was sentenced to life imprisonment for ordering the shooting of protesters in the revolution that ousted him.
On 13 January 2013, Egypt's Court of Cassation overturned Mubarak's sentence and ordered a retrial.
On retrial, Mubarak and his sons were convicted on 9 May 2015 of corruption and given prison sentences.
Mubarak was detained in a military hospital and his sons were freed 12 October 2015 by a Cairo court.
Egyptian military people
Egyptian Muslims
Presidents of Egypt
Prime Ministers of Egypt
Vice-Presidents of Egypt
Euclid of Alexandria  () (about 325 BC–265 BC) was a Greek mathematician who lived in Alexandria, Egypt and worked at the Library of Alexandria.
Little is known about this person, but people think he lived there when Ptolemy I was Pharaoh.
It is not known where and when he was born.
Euclid collected together all that was known of geometry, which is part of mathematics.
His Elements is the main source of ancient geometry.
Textbooks based on Euclid have been used up to the present day.
In the book, he starts out from a small set of axioms (that is, a group of things that everyone thinks are true).
Euclid then shows the properties of geometric objects and of whole numbers, based on those axioms.
The Elements also includes works on perspective, conic sections, spherical geometry, and possibly quadric surfaces.
Apart from geometry, the work also includes number theory.
Euclid came up with the idea of greatest common divisors.
They were in his Elements.
The greatest common divisor of two numbers is the greatest number that can fit evenly in both of the two numbers.
The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible.
Today that system is referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries which mathematicians developed in the 19th century.
In addition to the Elements, at least five works of Euclid have survived to the present day.
They follow the same logical structure as Elements, with definitions and proved propositions.
Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios.
It is similar to a third century AD work by Heron of Alexandria.
Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors.
The attribution to Euclid is doubtful.
Its author may have been Theon of Alexandria.
Phaenomena, a treatise on spherical astronomy, survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC.
Tributes to Euclid
An asteroid, is named after Euclid.
A crater on the moon is named after Euclid.
325 BC births
265 BC deaths
Number theorists
Guadeloupe is part of France in the Caribbean Sea.
It is made up of five islands.
The capital is Basse-Terre.
Arawak native Americans first lived on the islands.
Most died when Europeans came.
Guadeloupe was first governed by the French Company of the American Islands.
It was then taken over by England, given to Sweden, and given back to France.
71%: African or Multiracial (European, African, Chinese, East Indian, Amerindians, and others).
15%: East Indian
9%: European
2%: Middle Easterns
3%: Chinese
March 5 – Boston Massacre: 5 Americans killed by British troops in an event that would help start the American Revolutionary War 5 years later.
May 14 – Marie Antoinette arrives at the French court.
May 16 – 14-year old Marie Antoinette marries 15-year old Louis-Auguste (who later becomes Louis XVI King of France).
May 16 – Fireworks at the wedding of the crown prince of France in Paris cause a fire – 800 dead
June 3 – Gasper de Portola and Father Junipero Serra establish Monterey, which was the capital of California from 1777-1849.
July 1 – Comet Lexell (D/1770 L1) passes the Earth
August 22 – James Cook claimed for Great Britain the eastern coast of New Holland (Australia)
Joseph Priestley, British chemist, recommends the use of a rubber to remove pencil marks.
Joseph Louis Lagrange proves Bachet's Conjecture.
December 17 – Ludwig van Beethoven (baptised).
War between Austria and Venice.
May 25 – Carlo Dolci, Italian artist
April 23 – Miguel de Cervantes
April 23 – William Shakespeare, English playwright and poet
Lewis Allan "Lou" Reed (March 2, 1942 – October 27, 2013) was an American rock musician.
He was originally from Long Island, New York and spent most of his life in New York City.
He is remembered for being in the Velvet Underground, although he also released solo work.
He was friends with artist Andy Warhol.
Lewis Allan Reed was born on March 2, 1942 in Brooklyn, New York City.
He studied at Syracuse University.
Reed was raised Jewish.
Reed began his career in 1964.
He is perhaps most famous for his songs "Walk on the Wild Side" (about transgender woman Candy Darling and other such people Reed had known), "Perfect Day" (which was covered by many other artists, including Duran Duran and a version used by the BBC) and "Heroin" (an  "love song" about the drug.
Reed's 1989 album New York drew attention and praise, for its matter-of-fact look at the condition of New York City in the late 1980s.
At the height of his popularity as a solo artist, Reed released one of the least "commercial" recordings ever; his 1975 experimental album Metal Machine Music.
It was an hour of electric guitar feedback, and not what many people thought was music.
The album did not hurt his career in the long run, and it reminded people that Reed was a unique musician.
Because of his song about heroin, Reed was believed to have been addicted to the drug, but this was not the case.
He was a longtime user of amphetamines, marijuana and tobacco, but gradually stopped using any drugs.
He began exercising more, and enjoyed Tai Chi.
Reed was bisexual.
He was married to Betty Reed from 1973 until they divorced in 1978.
Then he was married to Sylvia Morales from 1980 until they divorced in 1994.
Then he was married to Laurie Anderson, the performance artist and musician, from 2008 until his death in 2013.
Reed had no children.
In April 2013, Reed had a liver transplant.
He died from a liver disease on October 27, 2013 in his home in Long Island, New York.
Tributes were paid to Reed on Twitter, including those from Miley Cyrus, Salman Rushdie, Samuel L. Jackson, Lenny Kravitz, Ricky Gervais, Ryan Adams, Elijah Wood, and many others.
John Cale, his Velvet Underground bandmate, posted on his Facebook: "The world has lost a fine songwriter and poet…I've lost my 'school-yard buddy'".
Official Lou Reed website
Comprehensive music biography of Reed by Allmusic
BBC obituary'
Deaths from liver disease
Disease-related deaths in New York
Albany Creek
Albany, Nova Scotia
Albany, Ontario
Albany, Prince Edward Island
Fort Albany, Ontario
Albany, New Zealand
Albany, South Africa
Albany, Tyne and Wear
Albany, Alabama
Albany, California,
Albany, Georgia,
Albany Park, Chicago, Illinois
Albany Township, Illinois
Albany, Indiana
Albany, Iowa
Albany Township, Maine
Albany, Minnesota
Albany Township, Minnesota
Albany Township, Nebraska
Albany, New Hampshire
Albany, New York, the capital of New York and the most populous city in this list
Albany, Ohio
Albany, Oklahoma
Albany Township, Berks County, Pennsylvania
Albany Township, Bradford County, Pennsylvania
Albany, Tennessee
Albany, Vermont
Albany River, in Canada
Duke of Albany, a Scottish, and later, British Peerage title
Albany Records, a record label in Albany, New York
Augusta, Western Australia
Shire of Augusta-Margaret River
Augusta, Ontario
North Augusta, Ontario
Augusta, Sicily, Italy
Augusta, Kansas
Augusta, Maine (capital city of Maine)
Augusta, Michigan
Augusta, Minnesota
Augusta, Missouri
Augusta, Montana
Augusta, New Jersey
Augusta, New York
Augusta, West Virginia
Augusta, Wisconsin
Augusta Charter Township, Michigan
Augusta Township, Lac qui Parle County, Minnesota
Augusta (given name)
Berkeley, California, USA
Cities in the United States
Charleston (dance), a dance
Charleston Battery, a soccer club based in Charleston, South Carolina
Anthropomorphism is the addition of human traits to something that is not a human.
For example, the non-human might have human feelings, needs, and wants.
It is common for people to use anthropomorphism.
Anthropomorphism is often used in stories and art.
The story of the "Three Little Pigs" has a wolf and three pigs who talk and act like humans.
Disney's Mickey Mouse also talks and acts like a human.
An anthropomorphized animal is called a "furry".
The novel The Call of the Wild also uses anthropomorphism.
The main character is a dog named Buck.
Many other characters are dogs and wolves.
In the story, the animals think and act more like humans than dogs.
Reasons for anthropomorphism
Humans can usually explain why humans do things.
Humans are not as good at explaining why non-human things do things.
This can lead to people assuming non-human things will do things like humans.
Humans learn about other humans early in life.
They know more about humans than about things that are not humans, and they can remember it better.
Furry: A section of anthropomorphism where animals and legendary creatures are shown as human-like in stories and art.
The apostrophe is a punctuation mark used in writing.
It is a diacritic (a mark used with letters).
To show where one or more letters have been left out, as in the abbreviation (contraction) of do not to don't.
To show the possessive case, as in the cat’s whiskers.
Its versus it's
The most common grammatical mistake in written English is to put it's where its is correct.
Its: a possessive adjective and pronoun of the personal pronoun it.
The cat chased its tail. (
correct)
The tyre lost it's grip. (
wrong)
It's: a contraction of the verbal phrase it is or it has.
It's mine. (
correct; check: It is mine)
It's been here. (
correct; check: It has been here)
The cat chased it's tail. (
wrong; cannot be expanded to it is)
The same applies to yours, theirs and ours because these are also possessive adjectives of personal pronouns.
The colour is ours.
That book is hers (or his).
Theirs was the responsibility.
Apostrophes are also used to show something belongs to someone (or something).
Again, correct uses can be expanded:
Mike's car. (
correct; the car that belongs to Mike)
The dog's ball. (
correct; the ball that belongs to the dog)
Those dog's are large. (
wrong; here "dogs" is a plural word)
The intrusive apostrophe
Comes in plurals which don't (do not) need it.
Do not put an apostrophe in word ending in s, such as a plural.
Put an apostrophe, or 's, at the end of the word instead.
Mr. Jones' hat or Mr. Jones's hat. (
both correct)
Both of my parents' birthdays. (
CD's and DVD's (wrong; not possessive.
See "Plural" section below)
Apple's and pear's (wrong; not possessive)
Writing dialogue or titles
or Li'l Bow Bow.
To make a word that doesn't (does not) usually exist as a plural into a plural, an apostrophe is occasionally used.
See these examples:
How many A's did you get this year?
Here it is wrong because it is not needed.
The poll received many yes's and very few no's.
Here it is sensible because without it the words 'yess' and 'nos' look quite peculiar.
However, you may find 'yeses' and 'noes' are appropriate as plurals.
General rule: if an apostrophe is not needed, do not use it.
Ryan M. North (born October 20, 1980) is a Canadian writer.
He is the author of the comic strip Dinosaur Comics, as well as Whispered Apologies and several other projects.
He is also the programmer of ohnorobot, a web comic search engine.
Ryan North is also a member of The Ryans, a group dedicated to being called Ryan and making comics.
Whispered Apologies
Canadian writers
Comics writers
A by-election or bye-election is a type of special election.
These elections are held in between general elections.
General elections are elections for all members of an elected body.
By-elections are elections for just some members.
A by-election could be needed if a member dies or resigns while in political office.
They are also used if a person is removed from office for some reason, for example if he/she is guilty of a crime or is not qualified to be a member anymore.
By-elections in the United States and the Philippines are called "special elections".
In India, they are called "bypolls".
In the 1980s, all 12 of the Unionist MPs in the British House of Commons resigned and all of the elections happened on the same day.
Although unusual, these were still only by-elections.
It is also defined as an election held in a single political constituency to fill a vacancy that has happened during a government's term of office.
Types of elections
By definition, the main task of a secretary is to keep organized paper and electronic files for the business, school, hospital, or government agency they work for.
Other common jobs that secretaries do are answering telephones; typing and writing letters; plan and schedule meetings with guests; and manage the website of their office.
In the past, most secretaries were men.
Today, 98% of secretaries are women, according to the US Census.
In 1952, several groups, for example the National Secretaries Association, founded Secretary's Day.
It is celebrated in the 4th week of April.
It has been renamed "Administrative Professional's Week" to represent the more challenging roles of secretaries today.
Other secretaries
In government, secretaries are important people who hold high positions in government.
Many secretaries in government are in charge of government agencies.
In the USA,  United States Secretary Defense is the head of the US Department of Defense.
Happiness is a feeling of pleasure and positivity.
When someone feels good, proud, excited, relieved or satisfied about something, that person is said to be "happy".
Feeling happy may help people to relax and to smile.
Happiness is usually thought of as the opposite of sadness.
However, it is very possible to feel both at once, often about different things, or sometimes even about the same thing You will feel some excited too when you are happy.
Happiness can also be inspired too.
Many philosophers have said that people in the world go back and forth between times of happiness and sadness, but there is nobody who is always happy or always sad.
Happiness sometimes causes people to cry when they laugh because the emotion takes control of them, people should learn how to be happy in life.
Happiness was thought of as the key to love in ancient civilizations such as the Incas and the Mayans.
6 is the first perfect number.
Its divisors (other than the number itself: 6) are 1, 2, and 3 and 1 + 2 + 3 equals 6.
Other perfect numbers include 28, 496 and 8128.
Perfect numbers that are even
Euclid discovered that the first four perfect numbers are generated by the formula 2n-1(2n - 1):
for n = 2:   21(22 - 1) = 6
for n = 3:   22(23 - 1) = 28
for n = 5:   24(25 - 1) = 496
for n = 7:   26(27 - 1) = 8128
Euclid saw that 2n - 1 is a prime number in these four cases.
He then proved that the formula 2n-1(2n - 1) gives an even perfect number whenever 2n - 1 is prime (Euclid, Prop.
IX.36).
Ancient mathematicians made many assumptions about perfect numbers based on the four they knew.
Most of the assumptions were wrong.
One of these assumptions was that since 2, 3, 5, and 7 are precisely the first four primes, the fifth perfect number would be obtained when n = 11, the fifth prime.
However, 211 - 1 = 2047 = 23 × 89 is not prime and therefore n = 11 does not give a perfect number.
Two other wrong assumptions were:
The fifth perfect number would have five digits since the first four had 1, 2, 3, and 4 digits respectively.
The perfect numbers would alternately end in 6 or 8.
The fifth perfect number () has 8 digits.
This falsifies the first assumption.
For the second assumption, the fifth perfect number indeed ends with a 6.
However, the sixth (8 589 869 056) also ends in a 6.
It is straightforward to show the last digit of any even perfect number must be 6 or 8.
In order for  to be prime, it is necessary that  should be prime.
Prime numbers of the form 2n - 1 are known as Mersenne primes, after the seventeenth-century monk Marin Mersenne, who studied number theory and perfect numbers.
Two millennia after Euclid, Euler proved that the formula 2n-1(2n - 1) will yield all the even perfect numbers.
Therefore, every Mersenne prime will yield a distinct even perfect number–there is a concrete one-to-one association between even perfect numbers and Mersenne primes.
This result is often referred to as the "Euclid-Euler Theorem".
Till January 2013, only 48 Mersenne primes are known.
This means there are 48 perfect numbers known, the largest being 257,885,160 × (257,885,161 - 1) with 34,850,340 digits.
The first 42 even perfect numbers are 2n-1(2n - 1) for
n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951
The other 7 known are for n = 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281.
It is still not known if there are infinitely many Mersenne primes and perfect numbers.
The search for new Mersenne primes is the goal of the GIMPS distributed computing project.
Since any even perfect number has the form 2n-1(2n - 1), it is a triangular number, and, like all triangular numbers, it is  the sum of all natural numbers up to a certain point; in this case: 2n - 1.
Also, any even perfect number except the first one is the sum of the first 2(n-1)/2 odd cubes:
Perfect numbers that are odd
It is not known whether there are any odd perfect numbers.
Various results have been obtained, but none that has helped to locate one or otherwise resolve the question of their existence.
Carl Pomerance  has presented a heuristic argument which suggests that no odd perfect numbers exist.
Also, it has been conjectured that there are no odd Ore's harmonic numbers.
If true, this would mean that there are no odd perfect numbers.
Any odd perfect number N must satisfy the following conditions:
N > 10300.
It is likely that, in the near future, it will be proven that N > 10500.
N is of the form
q, p1, ..., pk are distinct primes.
q ≡ α ≡ 1 (modulo 4) (Euler).
Let  be odd perfect number.
Since divisor function is multiplicative,
must be an even not divisible by 4 and all the remaining must be odd.
forces .
Either qα > 1020, or  > 1020 for some j (Cohen 1987).
N <  (Nielsen 2003).
The relation ≡ ...≡  ≡  1 (modulo 3) is not satisfied (McDaniel 1970).
The smallest prime factor of N is less than (2k + 8) / 3 (Grün 1952).
The largest prime factor of N is greater than 108 (Takeshi Goto and Yasuo Ohno, 2006).
The second largest prime factor is greater than 104, and the third largest prime factor is greater than 100 (Iannucci 1999, 2000).
N has at least 75 prime factors; and at least 9 distinct prime factors.
If 3 is not one of the factors of N, then N has at least 12 distinct prime factors (Nielsen 2006; Kevin Hare 2005).
Minor results
Even perfect numbers have a very precise form; odd perfect numbers are rare, if indeed they do exist.
There are a number of results on perfect numbers that are actually quite easy to prove but nevertheless superficially impressive; some of them also come under Richard Guy's Strong Law of Small Numbers:
Every odd perfect number is of the form 12m + 1 or 4356m + 1089 or 468m + 117 or 2916m + 729 (Roberts 2008).
An odd perfect number is not divisible by 105 (Kühnel 1949).
Every odd perfect number is the sum of two squares (Stuyvaert 1896).
A Fermat number cannot be a perfect number (Luca 2000).
The only even perfect number of the form　  is 28 (Makowski 1962).
By dividing the definition through by the perfect number N,  the reciprocals of the factors of a perfect number N must add up to 2:
For 6, we have ;
For 28, we have , etc.
The number of divisors of a perfect number (whether even or odd) must be even, since N cannot be a perfect square.
From these two results it follows that every perfect number is an Ore's harmonic number.
Related concepts
The sum of proper divisors gives various other kinds of numbers.
Numbers where the sum is less than the number itself are called deficient, and where it is greater than the number, abundant.
These terms, together with perfect itself, come from Greek numerology.
A pair of numbers which are the sum of each other's proper divisors are called amicable, and larger cycles of numbers are called sociable.
A positive integer such that every smaller positive integer is a sum of distinct divisors of it is a practical number.
Graeme L. Cohen, On the largest component of an odd perfect number, Journal of the Australian Mathematical Society, vol.
42 (1987), no.
280–286.
Euclid, Elements, Book IX, Proposition 36.
See D.E. Joyce's website for a translation and discussion of this proposition and its proof.
Takeshi Goto and Yasuo Ohno, Odd perfect numbers have a prime factor exceeding 108.
Preprint, 2006.
Available from Takeshi Goto's webpage "Largest prime factor of an odd perfect number".
Otto Grün, Über ungerade vollkommene Zahlen, Mathematische Zeitschrift, vol.
55 (1952), pp.
Kevin Hare, New techniques for bounds on the total number of prime factors of an odd perfect number.
Preprint, 2005.
Available from his webpage .
Douglas E. Iannucci, The second largest prime divisor of an odd perfect number exceeds ten thousand, Mathematics of Computation, vol.
68 (1999), no.
228, pp.
1749–1760.
Douglas E. Iannucci, The third largest prime divisor of an odd perfect number exceeds one hundred, Mathematics of Computation, vol.
69 (2000), no.
230, pages 867–879.
H.-J. Kanold, Untersuchungen über ungerade vollkommene Zahlen, Journal für die Reine und Angewandte Mathematik, vol.
183 (1941), pp.
98–109.
Ullrich Kühnel, Verschärfung der notwendigen Bedingungen für die Existenz von ungeraden vollkommenen Zahlen, "Mathematische Zeitschrift", vol.
52 (1949), 201—211.
Florian Luca, The anti-social Fermat number, Amer.
Monthly 107 (2000), pp.
W. L. McDaniel, The non-existence of odd perfect numbers of a certain form, Archiv der Mathematik (Basel), vol.
21 (1970), pp.
Pace P. Nielsen, "An upper bound for odd perfect numbers," Integers, vol.
3 (2003), A14, 9 pp.
Pace P. Nielsen, Odd perfect numbers have at least nine different prime factors, Mathematics of Computation, in press, 2006.
T. Roberts, "On the Form of an Odd Perfect Number", Australian Mathematical Gazette, 35:4 (2008), p244.
R. Steuerwald, Verschärfung einer notwendigen Bedingung für die Existenz einer ungeraden vollkommenen Zahl, S.-B. Bayer.
1937, pp.
Tomohiro Yamada, Odd perfect numbers of a special form, Colloq.
103 (2005), pp.
303–307.
David Moews: Perfect, amicable and sociable numbers
Perfect numbers - History and Theory
Perfect Number - from MathWorld
List of Perfect Numbers  at the On-Line Encyclopedia of Integer Sequences
List of known Perfect Numbers  All known perfect numbers are here.
OddPerfect.org  A projected distributed computing project to search for odd perfect numbers.
Integer sequences
StarCraft is a real-time strategy game for the PC.
It was created in 1998 by Blizzard Entertainment.
Starcraft is 14 years old and is still played by many people, in many countries around the world.
It is very popular in countries like Korea and the United States.
StarCraft and its expansion pack StarCraft: Brood War sold more than 1.5 million copies in 1998, making it the best selling game of the year.
In 1998, StarCraft won an Origins Award for best computer game.
On May 19, 2007 Blizzard announced that they are making StarCraft II.
Also, they have held some events for South Korean StarCraft pro-gamers to help them create the game.
The story is set in the future, where humans (called Terrans) get stuck in a war between two alien species, the Zerg and the Protoss.
The Zerg look like monsters, and are all controlled by a very powerful Zerg called the Overmind.
They fly around the universe and invade planets.
The Protoss, who have very advanced technology, look for the planets that the Zerg have taken over.
When they find a Zerg planet, they burn it so that the Zerg on that planet cannot spread to others.
In the original series human protagonist Jim Raynor and several Protoss allies attack and defeat the Overmind.
In Starcraft: Brood War Jim's ex-partner Sarah Kerrigan uses deceit and trickery to manipulate the Terran and Protoss into helping her take control of the entire Zerg brood, making her the strongest force in the galaxy.
StarCraft players can choose to play as Protoss, Zerg, or Terran races.
Each race has different soldiers and buildings.
Players can choose to play one-player or multiplayer games.
In both, the player must gather resources, and use them to build a base and make soldiers to attack the enemy.
The player wins when they destroy all the enemies buildings.
In one-player mode, there is the Campaign mode, and Custom mode.
In Campaign mode, the player goes through a series of missions, which tell the story.
Custom mode lets a player choose what race they want to be, what area they want to play on, and what race they will fight against (all enemies are controlled by the computer).
During a game, the player must use workers to gather minerals and vespene gas.
Minerals appear as blue crystals in the ground and vespene gas comes from a geyser that has green smoke coming out of it.
To gather vespene gas, the player needs to build a refinery building to be built on the geyser.
The player uses minerals and vespene gas they have gathered to construct buildings and create units to fight the enemy.
Buildings are structures that are used to create different kinds of units to fight the enemy.
In order to create units, players must build special structures or units that provide supply.
If the player does not have enough supply, they cannot create more units.
Each player has a supply limit of 200 units.
When the player has reached 200 units, they can not make more units.
There are many different buildings the player can construct.
Most of the buildings are used to build units.
There are other buildings that are used for research to upgrade units, making them more powerful.
Players can also make defensive buildings that are used to defend against attacking enemy units.
Each race have different types of units.
The Protoss have powerful warriors and machinery that cost lots of minerals and gas to build.
The Zerg use many fast and low cost units to defeat their enemies.
Terran units mix between Protoss and Zerg units.
They have strong, but easy to kill units that are powerful when used in formation.
No race in StarCraft is more powerful than another race.
Blizzard has released many small updates to the game that keep all the races balanced.
To win, players must gather and use resources wisely, and use smart strategies.
To become very skilled at the game, players also need to become good at micromanagement and macromanagement.
Macromanagement means collecting resources, building new bases, and making units to fight.
Micromanagement means moving units so they can use their abilities to protect each other and fight the enemy.
Players with better micromanagement will win fights against enemies who are not as good at micromanagement.
This makes StarCraft different from many newer games, because the newer games often do much of the micromanagement without the player having to do it.
StarCraft in South Korea
StarCraft is especially popular in South Korea.
In Korea, StarCraft sold 4.5 million copies, which is 40% of the total copies sold in the world.
Also, there are many pro gamers and pro gaming teams, so StarCraft games are broadcasted on TV and the internet.
The game was sold in Korea by LG Soft.
Even though the game wasn't translated into Korean, it was still very popular.
This problem was solved in 2005, with a new update to StarCraft.
StarCraft website
Brood War website
StarCraft Compendium
StarCraft News
News about StarCraft and StarCraft II
StarCraft 2 Forum  is a place where StarCraft 2 enthusiasts can gather and discuss all aspects of StarCraft 2.
starcraft 2 replays
Real-time strategy video games
MacOS games
One of the tough concerns of today's era is the Acid rain which can have a devastating effect over all organisms living on the Earth.
Acid rain is rain that is unusually acidic and  highly corrosive in nature.
It is rain with high levels of hydrogen ions (low pH).
It may be defined as "rain water having pH less than 5.6".
Acid rain can have harmful effects on plants, animals and humans.
It is caused when gaseous compounds of ammonium, carbon, nitrogen, and sulphur are released into the atmosphere.
The wind carries the gases high into the sky.
There the compounds react with the water in the atmosphere and acids are made.
In 1852, Robert Angus Smith showed the relationship between acid rain and atmospheric pollution in Manchester.
He coined the term "acid rain" in 1872.
Acid rain is caused by acids mixing with air.
The largest source of acid is sulphur dioxide.
Carbon dioxide and various oxides of nitrogen also make acid in the atmosphere.
These chemicals are both natural and artificial.
There are various natural causes, such as gases from volcanoes.
However, it is thought that air pollution by people now causes most acid rain.
People started producing more acidic gases when they started building factories and power stations.
These buildings as well as houses and vehicles burn coal or oil that have sulphur in them.
This releases gases into the air that produce acid rain.
Governments have tried since the 1970s to reduce the amount of sulphur being released into the Earth's atmosphere, and have had good results so far.
However, it is expensive to clean the smoke from factories and power stations.
In 2001 Great Britain still produced about five million tons of these gases every year; and China produced 18 million tons.
The United States produced more than 20 million tons then, which declined to 8.1 million in 2010.
Trees are destroyed by acid rain.
Fish are also killed by acid rain.
Acid rain can also be caused naturally.
For example, acids can be made by nitrogen compounds made by lightning, and volcanic eruptions can release sulphur dioxide into the atmosphere.
Acid rain has a devastating impact on forests, freshwater and soil.
It kills insect and aquatic life-forms as well as causes damage to buildings and having impacts on human health.
Due to the corrosive nature of the acids it damages both non-living things as well as living organisms.
Acid rain poisons rivers and lakes.
Fish and other animals cannot live in acid water.
It is also bad for buildings as the acid damages calcium carbonate stone.
The acid dissolves it.
Many buildings and monuments have been damaged by acid rain.
Acid rain is a regional air pollution problem.
Canada and North Western USA are worst affected.
The average pH of rainfall recorded in Toronto in Feb. 1979 was 3.5.
In 1989 fog in Los Angeles had a pH as low as 2.2.
However till now the record of having the most acidic rain is with US in Wheeling West Virginia where the pH was as low as 1.5.
Charlie Parker (August 29, 1920 in Kansas City, Missouri – March 12, 1955 in New York City), also known as "Bird" or "Yardbird", was considered one of the greatest jazz saxophonists, specifically alto saxophonist.
Parker was thought to have created bebop.
Musicians from Kansas City, Missouri
Mount Price information from Natural Resources Canada
Goldfinger is an American punk band.
It was founded in 1994.
They released their self-titled first album in 1996.
They were named after the Ian Fleming book and 1964 movie Goldfinger, based on the James Bond franchise.
John Feldmann - vocals, guitar
Charlie Paulson - gibson, fender, camel
Dangerous Darrin Pfeiffer - drums, vocals
Simon Williams - bass, vocals
Goldfinger - 1996
Hang ups - 1997
Stomping ground - 1999
Open your eyes - 2002
Disconnection notice - 2005
Hello destiny - 2008
Salamanca is a city in central Spain.
It is the capital city of the province with the same name.
The city has a very important university started in 1218.
It has two cathedrals and a famous Plaza Mayor (Main Square) built in the 18th century.
Frogs are a mascot of Salamanca.
Souvenirs of frogs can be found in almost every shop in the Plaza Mayor.
Official Tourist Information Office
Wiki of the city of Salamanca
General information on Salamanca
General information about events in Salamanca
Salamanca travel guide
Salamanca: Spain's answer to Oxford by The Guardian
Salamanca city guide at HitchHikers Handbook
Art Nouveau and Art Decó Museum Casa Lis
Car History Museum
Cathedral Museum
The Coptic Church of Ethiopia contacts the Roman Catholic Church for the first time.
The empire of the Maya breaks up into many little kingdoms.
The Ottoman Empire starts to become weak.
The Korean alphabet, the Hangul, is invented.
King Ivan III of Russia
King Edward IV of England
Margaret Beaufort, mother of Henry VII of England
Sandro Botticelli, Italian painter
Baeda Maryam of Ethiopia, king in the Solomonid dynasty.
Itzcóatl, Aztec ruler of Tenochtitlan
Jan van Eyck, Dutch painter
Christopher of Bavaria, King of Denmark, Norway and Sweden
The Tudor dynasty was a series of kings and queens of England.
This line of rulers started in 1485 and lasted until 1603.
The dynasty started when Henry Tudor defeated Richard III at the Battle of Bosworth Field.
This was the final stage of the Wars of the Roses and made him King Henry VII of England.
Arthur, Prince of Wales, was the oldest son of Henry VII and Elizabeth of York.
He married Catherine of Aragon.
She was the daughter of Ferdinand II of Argon and Isabella I of Castle).
Arthur died in 1502 and did not become King.
During her marriage to Henry VIII, Catherine had six children.
Only one of these children, Mary, survived.
When Catherine became too old to have any more children, Henry divorced her.
He then married a new wife, Anne Boleyn.
Henry and Boleyn also had a daughter, Elizabeth.
Anne Boleyn was executed in 1536.
Shortly after, Henry VIII married Jane Seymour of England.
She had one son, Edward VI of England, who would later become king himself at the age of 9.
Jane died in 1537.
Her death was caused by medical problems caused by Edward's birth.
Henry married three other wives before his death in 1547.
Edward, his only living son, became King after Henry died.
In 1553, Edward became ill.
He created the "Device for Succession.".
He said that his cousin, Lady Jane Grey, would be Queen after he died.
Lady Jane was only queen for nine days.
Henry's daughter, Mary I of England, was the next ruler of the Tudor dynasty.
Mary was a strong believer in Catholicism.
As Queen, Mary did many things against hundreds of Protestants.
Because of all the executions while she was Queen, she was given the nickname "Bloody Mary", which is a name for a modern cocktail today.
After Mary's death in 1558, her half-sister Elizabeth I of England became queen.
Unlike Mary, Elizabeth was a Protestant.
Elizabeth never married or had children.
Because she never married, Elizabeth is often called the "Virgin Queen".
The dynasty ended when Elizabeth died.
She had not named a person to be ruler after her death.
When she died, James I became King of England.
He was the son of Elizabeth's cousin, Mary Stuart.
This started the Stuart dynasty.
Religion in England
During the Tudor period, there were many changes in religion.
Henry VIII was a Catholic.
When the Pope said he could not divorce Catherine, Henry left Catholicism and named himself as head of the Church.
The Church of England was now Protestant.
Edward VI was raised a Protestant.
He closed all Catholic churches.
Mary I was a strong Catholic and heavily influenced by her Spanish mother Catherine of Aragon.
She closed the Protestant churches and burnt about 300 people for being Protestant.
Those people were later called martyrs.
Elizabeth was Protestant.
When she became queen, the Anglican Church was started.
Rulers of the Tudor dynasty
Henry VII of England (1485-1509)
Henry VIII of England (1509-1547)
Edward VI of England (1547-1553)
Lady Jane Grey (uncrowned) (1553) (deposed, died 1554)
Mary I of England (1553-1558)
Elizabeth I of England (1558-1603)
She was born in Bristol, England, on 3 February 1821.
When she was young, her family moved to America.
At first, she was a teacher.
She became a doctor in 1849.
She founded her own hospital in New York.
In 1874 she started a medical school for women in London with Sophie Jex-Blake and promoted women's rights.
An online history at the National Institutes of Health, including copies of historical documents
An online biography of Elizabeth Blackwell, with links to more articles on Blackwell and others in her famous family, plus links to many resources on the Internet
Biography from the National Institutes of Health
1821 births
American physicians
People from Somerset
Doom is a first-person shooter video game made by id Software in 1993.
It is one of the first games to use three-dimensional levels.
The game is about killing demons and zombies in order to stop an invasion.
Doom has traps, including crushing ceilings, radiation pools, and exploding barrels, that can kill the player.
Doom was also the first game with multiplayer deathmatch.
This means you can fight with other players instead of the demons and zombies.
The game was made with a computer language called C using some new techniques created by John Carmack.
It has five sequels: Doom 2 that came out in 1994, Final Doom that came out in 1996, Doom 3 that came out in 2004, Doom (2016), and Doom Eternal.
Doom is split into three basic components, the engine, the Iwad file, and the optional Pwad file.
The engine contains the code needed to run the game on a computer.
The Iwad file contains the default levels, sounds, pictures, and other components.
Pwad files contain custom levels.
The source code to the Doom engine was released in 1997 and can be downloaded for free.
The full 3-episode and 4-episode Iwad files have not been released for free and must still be purchased.
Doom is a shareware game of three episodes, each having eight standard levels and one secret level.
The secret level in each episode is accessed by finding a secret exit in one of the normal levels.
The episodes are Knee-Deep In The Dead, The Shores Of Hell and Inferno.
In the shareware version the only episode that can be played is Knee-Deep In The Dead.
The expansion pack of Doom is Ultimate Doom, which has the fourth episode, Thy Flesh Consumed.
In Doom, the player can carry and use many different weapons.
Each have their own special features and strengths.
They are your Fists, the Pistol, Shotgun, Chaingun, Rocket Launcher, Plasma Gun, BFG-9000, and Chainsaw.
The player gets new weapons by finding them in the level.
Most weapons can be found in more than one level.
Some weapons share ammo.
For example, both the Pistol and Chaingun use bullets, and the Plasma Gun and BFG both use energy cells.
The player must be careful not to waste ammo because if he or she does, there may be more than one weapon that cannot be used.
The Fists and Chainsaw do not have ammo limits, so the player can use them as long as they want.
Doom was also made for the SNES, Sega 32X, PlayStation, Sega Saturn, 3DO, Atari Jaguar, and Game Boy Advance.
It can also be downloaded online for the PlayStation 4, Xbox One, and Nintendo Switch.
1993 video games
Doom series
Sega 32X games
Sega Saturn games
The Jam was an English rock band formed in Woking, Surrey in 1972.
The members were Paul Weller (guitar, vocals), Bruce Foxton (bass guitar, vocals), and Rick Buckler (drums).
Having come out of from the short Punk movement they went on to become one of the UK's top bands.
They had four number one hits which were Going Underground, Start!,
Town Called Malice and Beat Surrender.
The Jam disbanded in 1982.
Lead singer Paul Weller went on to have hits with The Style Council during the remainder of the 1980s.
During the 1990s he had a successful solo career.
1972 establishments in the United Kingdom
Alchemy is the very old study and philosophy of how to change basic substances (such as metals) into other substances.
It also studied how substances (and how they are changed into other substances) were related to magic and astrology.
People who studied alchemy were called alchemists.
Some things alchemists tried to do were change lead or mercury into gold, make the philosopher's stone, and make the "elixir of life," which they thought could cure (make better) any disease and make someone young again.
Alchemists believed that substances, mind, philosophies, religion, magic and astrology were related to each other.
They tried to find connections between them.
They tried to understand one by understanding the other.
Some alchemists used metals (like gold or silver) to represent spiritual or occult ideas.
People in many different countries studied alchemy.
In the 1600s and 1700s, people started to study only the properties of substances without trying to relate them to secret, old knowledge.
They did experiments and wrote down what they discovered so other people could learn from them.
One of the important people who did these experiments was Robert Boyle.
People called the new study of substances chemistry.
Scientists have since discovered how to change one kind of element (the simplest kind of chemical substance) into another.
In 1980, an American scientist named Glenn Seaborg discovered how to change a very tiny amount of bismuth into gold with a nuclear reactor.
Making gold this way is much more difficult and expensive (costs a lot of money) than mining or recycling it.
Goldfinger is a 1964 spy movie based on the seventh James Bond book written by Ian Fleming.
Goldfinger is the third James Bond movie in the series.
It is also third to star Sean Connery as the British Secret Service agent James Bond.
Shirley Bassey sings the title song of the movie.
In this movie, the main bad guy is named Auric Goldfinger, and he likes gold a lot.