The Mathematics Portal
Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
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- ... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
- ... that Latvian-Soviet artist Karlis Johansons exhibited a skeletal tensegrity form of the Schönhardt polyhedron seven years before Erich Schönhardt's 1928 paper on its mathematics?
- ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
- ... that Fairleigh Dickinson's upset victory over Purdue was the biggest upset in terms of point spread in NCAA tournament history, with Purdue being a 23+1⁄2-point favorite?
- ... that The Math Myth advocates for American high schools to stop requiring advanced algebra?
- ... that ten-sided gaming dice have kite-shaped faces?
- ... that the prologue to The Polymath was written by Martin Kemp, a leading expert on Leonardo da Vinci?
- ... that Arithmetic was the first mathematics text book written in the Russian language?
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- ... that there are 115,200 solutions to the ménage problem of permuting six female-male couples at a twelve-person table so that men and women alternate and are seated away from their partners?
- ... that mathematician Paul Erdős called the Hadwiger conjecture, a still-open generalization of the four-color problem, "one of the deepest unsolved problems in graph theory"?
- ...that the six permutations of the vector (1,2,3) form a regular hexagon in 3d space, the 24 permutations of (1,2,3,4) form a truncated octahedron in four dimensions, and both are examples of permutohedra?
- ...that Ostomachion is a mathematical treatise attributed to Archimedes on a 14-piece tiling puzzle similar to tangram?
- ...that some functions can be written as an infinite sum of trigonometric polynomials and that this sum is called the Fourier series of that function?
- ...that the identity elements for arithmetic operations make use of the only two whole numbers that are neither composites nor prime numbers, 0 and 1?
- ...that as of April 2010 only 35 even numbers have been found that are not the sum of two primes which are each in a Twin Primes pair? ref
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e is the unique number such that the slope of y=ex (blue curve) is exactly 1 when x=0 (illustrated by the red tangent line). For comparison, the curves y=2x (dotted curve) and y=4x (dashed curve) are shown. Image credit: Dick Lyon |
The mathematical constant e is occasionally called Euler's number after the Swiss mathematician Leonhard Euler, or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms. It is one of the most important numbers in mathematics, alongside the additive and multiplicative identities 0 and 1, the imaginary unit i, and π, the circumference to diameter ratio for any circle. It has a number of equivalent definitions. One is given in the caption of the image to the right, and three more are:
- The sum of the infinite series
- where n! is the factorial of n, and 0! is defined to be 1 by convention.
- The global maximizer of the function
- The limit:
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The number e is also the base of the natural logarithm. Since e is transcendental, and therefore irrational, its value can not be given exactly. The numerical value of e truncated to 20 decimal places is 2.71828 18284 59045 23536. (Full article...)
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