Portal:Mathematics
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...)
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Did you know (autogenerated) –
 ... that in the aftermath of the American Civil War, the only Blackled organization providing teachers to formerly enslaved people was the African Civilization Society?
 ... that two members of the French parliament were killed when a delayedaction German bomb exploded in the town hall at Bapaume on 25 March 1917?
 ... that the 1914 Lubin vault fire in Philadelphia destroyed several thousand unique early silent films?
 ... that some philosophers of mathematics believe that the life cycle of a species of cicadas is a good argument for the existence of numbers?
 ... that museum director Alena Aladava rebuilt the Belarusian national art collection in the aftermath of the Second World War?
 ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
 ... that owner Matthew Benham influenced both Brentford FC in the UK and FC Midtjylland in Denmark to use mathematical modelling to recruit undervalued football players?
 ... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
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 ...that the Rule 184 cellular automaton can simultaneously model the behavior of cars moving in traffic, the accumulation of particles on a surface, and particleantiparticle annihilation reactions?
 ...that a cyclic cellular automaton is a system of simple mathematical rules that can generate complex patterns mixing random chaos, blocks of color, and spirals?
 ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
 ...that the axiom of choice is logically independent of the other axioms of Zermelo–Fraenkel set theory?
 ...that the Pythagorean Theorem generalizes to any three similar shapes on the three sides of a rightangled triangle?
 ...that the orthocenter, circumcenter, centroid and the centre of the ninepoint circle all lie on one line, the Euler line?
 ...that an arbitrary quadrilateral will tessellate?
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Example of a four color map Image credit: User:Inductiveload 
The four color theorem states that given any plane separated into regions, such as a political map of the counties of a state, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color. Two regions are called adjacent if they share a border segment, not just a point. "Color by Number" worksheets and exercises, which combine learning art and math for people of young ages, are a good example of the four color theorem.
It is often the case that using only three colors is inadequate. This applies already to the map with one region surrounded by three other regions (even though with an even number of surrounding countries three colors are enough) and it is not at all difficult to prove that five colors are sufficient to color a map.
The four color theorem was the first major theorem to be proven using a computer, and the proof is disputed by some mathematicians because it would be infeasible for a human to verify by hand (see computeraided proof). Ultimately, in order to believe the proof, one has to have faith in the correctness of the compiler and hardware executing the program used for the proof.
The lack of mathematical elegance was another factor, and to paraphrase comments of the time, "a good mathematical proof is like a poem — this is a telephone directory!" (Full article...)
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