Portal:Mathematics/Did you know archive

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This page is an archive of Did You Know facts featured on the Mathematics Wikiportal. (Items are added here when they first appear on the main portal page).

[edit] 2005

• that René Descartes, Father of Modern Mathematics, was also an influential philosopher who coined the phrase I think, therefore I am?
• that the discovery of calculus is credited to Gottfried Wilhelm Leibniz and Isaac Newton?
• that the first calculator able to perform the same functions as the slide rule was the 1972 HP-35?
• that Ptolemy, an influential greek mathematician, believed that everything was related to Mathematics?
• that modern linear algebra dates back to the early 1840s?
• that Archimedes is said to have celebrated a discovery about the principles of density and buoyancy by getting out of his bathtub and running into the street (having forgotten that he was naked), shouting "Eureka!"?
• that the golden ratio, often denoted by the Greek letter φ, can be found in many instances of geometry?
• that chaos theory has expanded greatly in the past 30 years thanks to the exponential growth of computing power as predicted by Moore's law?
• that Lindenmayer systems are able to simulate the growth processes of plants using very simple rules?
• that Euler's identity links five important mathematical constants?
• that the equal sign, or =, was invented in 1557 by the Welsh mathematician Robert Recorde?
• that π (pi) was first calculated theoretically, rather than by construction, by Archimedes in the Third century BC?
• that the number 0 was invented separately in India and by the Maya?

[edit] 2006

• ...that decimal system originated in India?
• ...that there is a 4-dimensional cube called a tesseract?
• ...that Chaitin's constant Ω is a real number which is definable but not computable?
• ...that it is possible to turn a sphere inside out without tears or creases? (The sphere is allowed to pass through itself).
• ...that the Riemann hypothesis is one of the most important unsolved problems in mathematics, and has a $1,000,000 prize for a proof or disproof?
• ...that the set of rational numbers is equal in size to the subset of integers; that is, they can be put in one-to-one correspondence?
• ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.
• ...that it is unknown whether π and e are algebraically independent over the rationals?
• ...that Henri Poincaré is often described as the last "universalist" capable of understanding and contributing in virtually all parts of mathematics?
• ...that Fermat's Last Theorem was unsolved for more than three hundred years?
• ...that Euler found 59 more pairs of amicable numbers while for 2000 years, only 3 pairs had been found before him?
• ...that trying to find a proof by contradiction to Euclid's parallel postulate, geometers were led to the creation of two new types of non-euclidean geometry, hyperbolic geometry and elliptic geometry?
• ...that 6 is the second smallest composite number, a highly composite number, a harmonic divisor number, and the first unitary perfect number, perfect number and hyperperfect number?
• ...that it is impossible to square a circle using only a compass and straightedge?
• ...that it is impossible to devise a single formula involving only polynomials and radicals for solving an arbitrary quintic equation?
• ...that the Klein Bottle gives a two-fold covering space of itself?
• ...that a sphere can be cut up into finitely many pieces and reassembled into two spheres the same size as the original (Banach-Tarski paradox)?
• ...that the Catalan numbers solve a number of problems in combinatorics such as the number of ways to completely parenthesize an algebraic expression with n+1 factors?
• ...that a regular heptagon is the regular polygon with the least number of sides which is not constructible with a compass and straightedge?
• ...that the Gudermannian function relates the regular trigonometric functions and the hyperbolic trigonometric functions without the use of complex numbers?
• ...that outstanding mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?
• ...that you cannot knot strings in 4-dimensions? You can, however, knot 2-dimensional surfaces like spheres.
• ...that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type the complete works of William Shakespeare.