Portal:Mathematics
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 after Florida schools banned 54 mathematics books, Chaz Stevens petitioned that they also ban the Bible?
- ... that two members of the French parliament were killed when a delayed-action German bomb exploded in the town hall at Bapaume on 25 March 1917?
- ... 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 in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
- ... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
- ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
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- ...an infinite, nonrepeating decimal can be represented using only the number 1 using continued fractions?
- ...that 253931039382791 and the following 18 prime numbers all end in the digit 1?
- ...that the Electronic Frontier Foundation funds awards for the discovery of prime numbers beyond certain sizes?
- ...that pi can be computed using only the number 2 by the work of Viète?
- … that the Riemann Hypothesis, one of the Millennium Problems, depends on the asymptotic growth of the Mertens Function?
- … that every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater?
- … that the best known lower bound for the length of the smallest superpermutation was first posted anonymously to the internet imageboard 4chan?
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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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