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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Example of a Persian design with wallpaper group type "p6m" Image credit: Owen Jones 
A wallpaper group is a mathematical concept used to classify repetitive designs on twodimensional surfaces, such as floors and walls, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. The mathematical study of such patterns reveals that exactly 17 different types of pattern can occur.
Wallpaper groups are examples of an abstract algebraic structure known as a group. Groups are frequently used in mathematics to study the notion of symmetry. Wallpaper groups are related to the simpler frieze groups, and to the more complex threedimensional crystallographic groups.
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A hypotrochoid is a curve traced out by a point "attached" to a smaller circle rolling around inside a fixed larger circle. In this example, the hypotrochoid is the red curve that is traced out by the red point 5 units from the center of the black circle of radius 3 as it rolls around inside the blue circle of radius 5. A special case is a hypotrochoid with the inner circle exactly onehalf the radius of the outer circle, resulting in an ellipse (see an animation showing this). Mathematical analysis of closelyrelated curves called hypocycloids lead to special Lie groups. Both hypotrochoids and epitrochoids (where the moving circle rolls around on the outside of the fixed circle) can be created using the Spirograph drawing toy. These curves have applications in the "real world" in epicyclic and hypocycloidal gearing, which were used in World War II in the construction of portable radar gear and may be used today in 3D printing.
Did you know...
 ... if the integer n is prime, then the nth Perrin number is divisible by n?
 ...that it is impossible to trisect a general angle using only a ruler and a compass?
 ...that in a group of 23 people, there is a more than 50% chance that two people share a birthday?
 ...that statistical properties dictated by Benford's Law are used in auditing of financial accounts as one means of detecting fraud?
 ...the hyperbolic trigonometric functions of the natural logarithm can be represented by rational algebraic fractions?
 ... that economists blame market failures on nonconvexity?
 ... that, according to the pizza theorem, a circular pizza that is sliced offcenter into eight equalangled wedges can still be divided equally between two people?
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