WikiPortallus:

Culture · Geography · Health · History · Mathematics · Nature · Philosophy · Religion · Society · Technology

The Mathematics Portal

Mathematics is the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations. It evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of positions, shapes and motions of physical objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.

There are approximately 19639 mathematical articles in Wikipedia.

Show new selections

Selected article

3D illustration of a stereographic projection from the north pole onto a plane below the sphere.

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point — the projection point. Where it is defined, the mapping is smooth and bijective. It is also conformal, meaning that it preserves angles. On the other hand, it does not preserve area, especially near the projection point.

Intuitively, then, the stereographic projection is a way of picturing the sphere as the plane, with some inevitable compromises. Because the sphere and the plane appear in many areas of mathematics and its applications, so does the stereographic projection; it finds use in diverse fields including differential geometry, complex analysis, cartography, geology, and crystallography.

...Archive

Image credit: Mark Howison

Read more...

Picture of the month

Credit: Jtico

In projective geometry, Desargues' theorem, named in honor of Gérard Desargues, states:

In a projective space, two triangles are in perspective axially if and only if they are in perspective centrally.

The above picture illustrates Desargues' theorem. Another important feature of projective geometry noticable in the picture is all lines meet at exactly one point (e.g. there are no parallel lines).

...Archive

Read more...

Did you know...

...that a sphere can be cut up and reassembled into two spheres the same size as the original (Banach-Tarski paradox)?
...that it is impossible to devise a single formula involving only polynomials and radicals for solving an arbitrary quintic equation?
...that Euler found 59 more amicable numbers while for 2000 years, only 3 pairs had been found before him?
...that you cannot knot strings in 4-dimensions? You can, however, knot 2-dimensional surfaces like spheres.
...that there are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?
...that there are different sizes of infinite sets in set theory? More precisely, not all infinite cardinal numbers are equal?
...that every natural number can be written as the sum of four squares?
...that the largest known prime is over 9 million digits long?
...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?

Showing 9 items out of 21

More did you know

WikiProjects

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

Project pages

Subprojects

Related projects

Things you can do

Topics in mathematics

General	Foundations	Number theory	Discrete mathematics
Mathematicians History of mathematics Philosophy of mathematics Mathematical notation Mathematical beauty Mathematics education Areas of mathematics	Foundations of mathematics Set theory (portal) Naive set theory Axiomatic set theory Mathematical logic Proof theory Model theory Category theory (portal) Topos theory Gödel's incompleteness theorems	Number theory (portal) Algebraic number theory Analytic number theory Arithmetic Numbers Natural numbers Prime numbers Rational numbers Algebraic numbers Fundamental theorem of arithmetic	Discrete mathematics (portal) Combinatorics Graph theory Game theory Discrete geometry Theoretical computer science Computability theory Complexity theory Information theory
Analysis	Algebra	Geometry and topology	Applied mathematics
Analysis (portal) Calculus Vector calculus Differential equations Calculus of variations Real analysis Complex analysis Functional analysis Measure theory Harmonic analysis Special functions Fundamental theorem of calculus	Algebra (portal) Elementary algebra Abstract algebra Group theory Ring theory Field theory Commutative algebra Linear algebra Matrix theory Multilinear algebra Universal algebra Order theory Fundamental theorem of algebra	Geometry (portal) Topology (portal) General topology Algebraic topology Geometric topology Euclidean geometry Non-Euclidean geometry Affine geometry Projective geometry Differential geometry Riemannian geometry Lie groups Algebraic geometry Trigonometry	Applied mathematics Numerical analysis Mathematical biology Optimization Dynamical systems Chaos theory Financial mathematics Cryptography (portal) Mathematical physics Classical mechanics Probability Statistics Stochastic processes Operations research

Index of mathematics articles

ARTICLE INDEX:	A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 0-9
MATHEMATICIANS:	A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Related portals


Algebra	Analysis	Category theory	Computer science	Cryptography	Discrete mathematics	Geometry

Logic	Mathematics	Number theory	Physics	Science	Set theory	Topology