Jump to content

Portal:Mathematics

Page semi-protected
From Wikipedia, the free encyclopedia

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...)

  Featured articles are displayed here, which represent some of the best content on English Wikipedia.

Selected image – show another

animation of a grid of boxes numbered 2 through 120, where the prime numbers are progressively circled and listed to the side while the composite numbers are struck out
animation of a grid of boxes numbered 2 through 120, where the prime numbers are progressively circled and listed to the side while the composite numbers are struck out
The sieve of Eratosthenes is a simple algorithm for finding all prime numbers up to a specified maximum value. It works by identifying the prime numbers in increasing order while removing from consideration composite numbers that are multiples of each prime. This animation shows the process of finding all primes no greater than 120. The algorithm begins by identifying 2 as the first prime number and then crossing out every multiple of 2 up to 120. The next available number, 3, is the next prime number, so then every multiple of 3 is crossed out. (In this version of the algorithm, 6 is not crossed out again since it was just identified as a multiple of 2. The same optimization is used for all subsequent steps of the process: given a prime p, only multiples no less than p2 are considered for crossing out, since any lower multiples must already have been identified as multiples of smaller primes. Larger multiples that just happen to already be crossed out—like 12 when considering multiples of 3—are crossed out again, because checking for such duplicates would impose an unnecessary speed penalty on any real-world implementation of the algorithm.) The next remaining number, 5, is the next prime, so its multiples get crossed out (starting with 25); and so on. The process continues until no more composite numbers could possibly be left in the list (i.e., when the square of the next prime exceeds the specified maximum). The remaining numbers (here starting with 11) are all prime. Note that this procedure is easily extended to find primes in any given arithmetic progression. One of several prime number sieves, this ancient algorithm was attributed to the Greek mathematician Eratosthenes (d. c. 194 BCE) by Nicomachus in his first-century (CE) work Introduction to Arithmetic. Other more modern sieves include the sieve of Sundaram (1934) and the sieve of Atkin (2003). The main benefit of sieve methods is the avoidance of costly primality tests (or, conversely, divisibility tests). Their main drawback is their restriction to specific ranges of numbers, which makes this type of method inappropriate for applications requiring very large prime numbers, such as public-key cryptography.

Good articles – load new batch

  These are Good articles, which meet a core set of high editorial standards.

Did you know (auto-generated)load new batch

More did you know – view different entries

Did you know...
Did you know...
Showing 7 items out of 75

Selected article – show another


A pentagram colored to distinguish its line segments of different lengths. The four lengths are in golden ratio to one another
Image credit: User:PAR

In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is a mathematical constant, usually denoted by the Greek letter φ (phi).

Expressed algebraically, two quantities a and b (assuming ) are therefore in the golden ratio if

It follows from this property that φ satisfies the quadratic equation φ2 = φ + 1 and is therefore an algebraic irrational number, given by

which is approximately equal to 1.6180339887.

At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.

Other names frequently used for or closely related to the golden ratio are golden section (Latin: sectio aurea), golden mean, golden number, divine proportion (Italian: proporzionedivina), divine section (Latin: sectio divina), golden proportion, golden cut, and mean of Phidias. (Full article...)

View all selected articles

Subcategories


Full category tree. Select [►] to view subcategories.

Topics in mathematics

General Foundations Number theory Discrete mathematics


Algebra Analysis Geometry and topology Applied mathematics
Source

Index of mathematics articles

ARTICLE INDEX:
MATHEMATICIANS:

WikiProjects

WikiProjects The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page.

In other Wikimedia projects

The following Wikimedia Foundation sister projects provide more on this subject:

More portals