Portal:Mathematics
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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.
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There are approximately 31,444 mathematics articles in Wikipedia.
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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.
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A Bézier curve is a parametric curve important in computer graphics and related fields. Widely publicized in 1962 by the French engineer Pierre Bézier, who used them to design automobile bodies, the curves were first developed in 1959 by Paul de Casteljau using de Casteljau's algorithm. In this animation, a quartic Bézier curve is constructed using control points P_{0} through P_{4}. The green line segments join points moving at a constant rate from one control point to the next; the parameter t shows the progress over time. Meanwhile, the blue line segments join points moving in a similar manner along the green segments, and the magenta line segment points along the blue segments. Finally, the black point moves at a constant rate along the magenta line segment, tracing out the final curve in red. The curve is a fourthdegree function of its parameter. Quadratic and cubic Bézier curves are most common since higherdegree curves are more computationally costly to evaluate. When more complex shapes are needed, lowerorder Bézier curves are patched together. For example, modern computer fonts use Bézier splines composed of quadratic or cubic Bézier curves to create scalable typefaces. The curves are also used in computer animation and video games to plot smooth paths of motion. Approximate Bézier curves can be generated in the "real world" using string art.
Did you know...
 ...that statistical properties dictated by Benford's Law are used in auditing of financial accounts as one means of detecting fraud?
 ...that Modular arithmetic has application in at least ten different fields of study, including the arts, computer science, and chemistry in addition to mathematics?
 ... that according to Kawasaki's theorem, an origami crease pattern with one vertex may be folded flat if and only if the sum of every other angle between consecutive creases is 180º?
 ... that, in the Rule 90 cellular automaton, any finite pattern eventually fills the whole array of cells with copies of itself?
 ... that, while the crisscross algorithm visits all eight corners of the Klee–Minty cube when started at a worst corner, it visits only three more corners on average when started at a random corner?
 ...that in senary, all prime numbers other than 2 and 3 end in 1 or a 5?
 ... if the integer n is prime, then the nth Perrin number is divisible by n?
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