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


Polar graph paper.svg
A polar grid with several angles labeled
Image credit: User:Mets501

The polar coordinate system is a two-dimensional coordinate system in which points are given by an angle and a distance from a central point known as the pole (equivalent to the origin in the more familiar Cartesian coordinate system). The polar coordinate system is used in many fields, including mathematics, physics, engineering, navigation and robotics. It is especially useful in situations where the relationship between two points is most easily expressed in terms of angles and distance; in the Cartesian coordinate system, such a relationship can only be found through trigonometric formulae. For many types of curves, a polar equation is the simplest means of representation of variables.

It is known that the Greeks used the concepts of angle and radius. The astronomer Hipparchus (190-120 BC) tabulated a table of chord functions giving the length of the chord for each angle, and there are references to his using polar coordinates in establishing stellar positions.

View all selected articlesRead More...

Selected image

illustration of a closed loop (a circle) and progressively more knotted loops
Credit: Jkasd

This is a chart of all prime knots having seven or fewer crossings (not including mirror images) along with the unknot (or "trivial knot"), a closed loop that is not a prime knot. The knots are labeled with Alexander-Briggs notation. Many of these knots have special names, including the trefoil knot (31) and figure-eight knot (41). Knot theory is the study of knots viewed as different possible embeddings of a 1-sphere (a circle) in three-dimensional Euclidean space (R3). These mathematical objects are inspired by real-world knots, such as knotted ropes or shoelaces, but don't have any free ends and so cannot be untied. (Two other closely related mathematical objects are braids, which can have loose ends, and links, in which two or more knots may be intertwined.) One way of distinguishing one knot from another is by the number of times its two-dimensional depiction crosses itself, leading to the numbering shown in the diagram above. The prime knots play a role very similar to prime numbers in number theory; in particular, any given (non-trivial) knot can be uniquely expressed as a "sum" of prime knots (a series of prime knots spliced together) or is itself prime. Early knot theory enjoyed a brief period of popularity among physicists in the late 19th century after William Thomson suggested that atoms are knots in the luminiferous aether. This led to the first serious attempts to catalog all possible knots (which, along with links, now number in the billions). In the early 20th century, knot theory was recognized as a subdiscipline within geometric topology. Scientific interest was resurrected in the latter half of the 20th century by the need to understand knotting problems in organic chemistry, including the behavior of DNA, and the recognition of connections between knot theory and quantum field theory.

Did you know…

Did you know...

             

Showing 7 items out of 74

WikiProjects

Things you can do

Categories


Topics in mathematics

GeneralFoundationsNumber theoryDiscrete mathematics
Nuvola apps bookcase.svg
Set theory icon.svg
Nuvola apps kwin4.png
Nuvola apps atlantik.png


AlgebraAnalysisGeometry and topologyApplied mathematics
Arithmetic symbols.svg
Source
Nuvola apps kpovmodeler.svg
Gcalctool.svg

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

In other Wikimedia projects

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

Commons
Media

Wikinews 
News

Wikiquote 
Quotations

Wikisource 
Texts

Wikiversity
Learning resources

Wiktionary 
Definitions

Wikidata 
Database

Other Languages
አማርኛ: በር:ሒሳብ
Bân-lâm-gú: Portal:Sò͘-ha̍k
беларуская (тарашкевіца)‎: Партал:Матэматыка
한국어: 포털:수학
Bahasa Indonesia: Portal:Matematika
interlingua: Portal:Mathematica
Kiswahili: Lango:Hisabati
Kreyòl ayisyen: Pòtay:matematik
македонски: Портал:Математика
Bahasa Melayu: Portal:Matematik
မြန်မာဘာသာ: Portal:သင်္ချာ
Nederlands: Portaal:Wiskunde
日本語: Portal:数学
oʻzbekcha/ўзбекча: Portal:Matematika
português: Portal:Matemática
slovenčina: Portál:Matematika
Soomaaliga: Portal:Xisaab
српски / srpski: Портал:Математика
Taqbaylit: Awwur:Tusnakt
татарча/tatarça: Портал:Математика
українська: Портал:Математика
Tiếng Việt: Chủ đề:Toán học
文言: 門:數學