Portal:Mathematics

Portal topics: Activities; Culture; Geography; Health; History; Mathematics; Nature; People; Philosophy; Religion; Society; Technology; Random portal

The Mathematics Portal

P:MAT

Mathematics is the study of numbers, quantity, space, structure, and change. 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.

More about Mathematics...

There are approximately 31,444 mathematics articles in Wikipedia.

Refresh with new selections below (purge)

edit

Selected article

e is the unique number such that the slope of y=e^x (blue curve) is exactly 1 when x=0 (illustrated by the red tangent line). For comparison, the curves y=2^x (dotted curve) and y=4^x (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
${\begin{aligned}e&=\sum _{n=0}^{\infty }{\frac {1}{n!}}\\&={\frac {1}{0!}}+{\frac {1}{1!}}+{\frac {1}{2!}}+{\frac {1}{3!}}+\cdots \\\end{aligned}}$

where n! is the factorial of n, and 0! is defined to be 1 by convention.
The global maximizer of the function
$f(x)=x^{1 \over x}.$
The limit:
$e=\lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}$

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.

View all selected articles

Read More...

edit

Selected image

Credit: Phil Tregoning

A Bézier curve is a parametric curve important in computer graphics and related fields. Widely publicized in 1962 by the French engineer Pierre Bézier, who used them to design automobile bodies, the curves were first developed in 1959 by Paul de Casteljau using de Casteljau's algorithm. In this animation, a quartic Bézier curve is constructed using control points P₀ through P₄. The green line segments join points moving at a constant rate from one control point to the next; the parameter $t$ shows the progress over time. Meanwhile, the blue line segments join points moving in a similar manner along the green segments, and the magenta line segment points along the blue segments. Finally, the black point moves at a constant rate along the magenta line segment, tracing out the final curve in red. The curve is a fourth-degree function of its parameter. Quadratic and cubic Bézier curves are most common since higher-degree curves are more computationally costly to evaluate. When more complex shapes are needed, lower-order Bézier curves are patched together. For example, modern computer fonts use Bézier splines composed of quadratic or cubic Bézier curves to create scalable typefaces. The curves are also used in computer animation and video games to plot smooth paths of motion. Approximate Bézier curves can be generated in the "real world" using string art.

More selected pictures... Read more...

edit

Did you know…

...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 outstanding mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?
...that a regular heptagon is the regular polygon with the fewest 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 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 ball can be cut up and reassembled into two balls the same size as the original (Banach-Tarski paradox)?