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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- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
- ... that after Florida schools banned 54 mathematics books, Chaz Stevens petitioned that they also ban the Bible?
- ... that the number of cannonballs in a square pyramid with cannonballs along each edge is ?
- ... that mathematician Mathias Metternich was one of the founders of the Jacobin club of the Republic of Mainz?
- ... that Latvian-Soviet artist Karlis Johansons exhibited a skeletal tensegrity form of the Schönhardt polyhedron seven years before Erich Schönhardt's 1928 paper on its mathematics?
- ... that ten-sided gaming dice have kite-shaped faces?
- ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
- ... that despite a mathematical model deeming the ice cream bar flavour Goody Goody Gum Drops impossible, it was still created?
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- ...the hyperbolic trigonometric functions of the natural logarithm can be represented by rational algebraic fractions?
- ... that economists blame market failures on non-convexity?
- ... that, according to the pizza theorem, a circular pizza that is sliced off-center into eight equal-angled wedges can still be divided equally between two people?
- ... that the clique problem of programming a computer to find complete subgraphs in an undirected graph was first studied as a way to find groups of people who all know each other in social networks?
- ... that the Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle?
- ... that the Life without Death cellular automaton, a mathematical model of pattern formation, is a variant of Conway's Game of Life in which cells, once brought to life, never die?
- ... that one can list every positive rational number without repetition by breadth-first traversal of the Calkin–Wilf tree?
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Banach–Tarski paradox Image credit: Benjamin D. Esham |
The Banach–Tarski paradox is a theorem in set-theoretic geometry which states that a solid ball in 3-dimensional space can be split into a finite number of non-overlapping pieces, which can then be put back together in a different way to yield two identical copies of the original ball. The reassembly process involves only moving the pieces around and rotating them, without changing their shape. However, the pieces themselves are complicated: they are not usual solids but infinite scatterings of points. A stronger form of the theorem implies that given any two "reasonable" solid objects (such as a small ball and a huge ball) — solid in the sense of the continuum — either one can be reassembled into the other. This is often stated colloquially as "a pea can be chopped up and reassembled into the Sun". (Full article...)
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