Portal:Mathematics
The Mathematics Portal
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.
Selected article  Selected picture  Did you know...  Topics in mathematics
Categories  WikiProjects  Things you can do  Index  Related portals
There are approximately 31,444 mathematics articles in Wikipedia.
Selected article
A dodecahedron, one of the five Platonic solids Image credit: User:DTR 
A regular polytope is a geometric figure with a high degree of symmetry. Examples in two dimensions include the square, the regular pentagon and hexagon, and so on. In three dimensions the regular polytopes include the cube, the dodecahedron, and all other Platonic solids. Other Platonic solids include the tetrahedron, the octahedron, the icosahedron. Examples exist in higher dimensions also, such as the 5dimensional hendecatope. Circles and spheres, although highly symmetric, are not considered polytopes because they do not have flat faces. The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both nonmathematicians and mathematicians.
Many regular polytopes, at least in two and three dimensions, exist in nature and have been known since prehistory. The earliest surviving mathematical treatment of these objects comes to us from ancient Greek mathematicians such as Euclid. Indeed, Euclid wrote a systematic study of mathematics, publishing it under the title Elements, which built up a logical theory of geometry and number theory. His work concluded with mathematical descriptions of the five Platonic solids.
View all selected articles  Read More... 
Selected picture
This image illustrates a failed attempt to comb the "hair" on a ball flat, leaving a tuft sticking out at each pole. The hairy ball theorem of algebraic topology states that whenever one attempts to comb a hairy ball, there will always be at least one point on the ball at which a tuft of hair sticks out. More precisely, it states that there is no nonvanishing continuous tangentvector field on an evendimensional n‑sphere (an ordinary sphere in threedimensional space is known as a "2sphere"). This is not true of certain other threedimensional shapes, such as a torus (doughnut shape) which can be combed flat. The theorem was first stated by Henri Poincaré in the late 19th century and proved in 1912 by L. E. J. Brouwer. If one idealizes the wind in the Earth's atmosphere as a tangentvector field, then the hairy ball theorem implies that given any wind at all on the surface of the Earth, there must at all times be a cyclone somewhere. Note, however, that wind can move vertically in the atmosphere, so the idealized case is not meteorologically sound. (What is true is that for every "shell" of atmosphere around the Earth, there must be a point on the shell where the wind is not moving horizontally.) The theorem also has implications in computer modeling (including video game design), in which a common problem is to compute a nonzero 3D vector that is orthogonal (i.e., perpendicular) to a given one; the hairy ball theorem implies that there is no single continuous function that accomplishes this task.
Did you know...
 ... that one can list every positive rational number without repetition by breadthfirst traversal of the Calkin–Wilf tree?
 ... that the Hadwiger conjecture implies that the external surface of any threedimensional convex body can be illuminated by only eight light sources, but the best proven bound is that 16 lights are sufficient?
 ... that an equitable coloring of a graph, in which the numbers of vertices of each color are as nearly equal as possible, may require far more colors than a graph coloring without this constraint?
 ... that no matter how biased a coin one uses, flipping a coin to determine whether each edge is present or absent in a countably infinite graph will always produce the same graph, the Rado graph?
 ...that it is possible to stack identical dominoes off the edge of a table to create an arbitrarily large overhang?
 ...that in Floyd's algorithm for cycle detection, the tortoise and hare move at very different speeds, but always finish at the same spot?
 ...that in graph theory, a pseudoforest can contain trees and pseudotrees, but cannot contain any butterflies, diamonds, handcuffs, or bicycles?
WikiProjects
The Mathematics WikiProject is the center for mathematicsrelated editing on Wikipedia. Join the discussion on the project's talk page.
Project pages
Essays
Subprojects
Related projects
Things you can do
Categories
Algebra  Arithmetic  Analysis  Complex analysis  Applied mathematics  Calculus  Category theory  Chaos theory  Combinatorics  Dynamic systems  Fractals  Game theory  Geometry  Algebraic geometry  Graph theory  Group theory  Linear algebra  Mathematical logic  Model theory  Multidimensional geometry  Number theory  Numerical analysis  Optimization  Order theory  Probability and statistics  Set theory  Statistics  Topology  Algebraic topology  Trigonometry  Linear programming
Mathematics (books)  History of mathematics  Mathematicians  Awards  Education  Literature  Notation  Organizations  Theorems  Proofs  Unsolved problems
Topics in mathematics
General  Foundations  Number theory  Discrete mathematics 



Algebra  Analysis  Geometry and topology  Applied mathematics 
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  Statistics  Topology 
 What are portals?
 List of portals