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?
...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?
...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 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 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 Field's Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?
... you cannot knot strings in 4-dimensions? You can, however, knot 2-dimensional surfaces like spheres.

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Portal:Mathematics/Did you know archive

From Wikipedia, the free encyclopedia

[edit] 2005

[edit] 2006

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