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A 4-state two-dimensional Turing machine invented in the 1980s. The ant starts out on a grid containing black and white cells, and then follows the following set of rules. 1. ...

Marion's theorem (Mathematics Teacher 1993, Maushard 1994, Morgan 1994) states that the area of the central hexagonal region determined by trisection of each side of a ...

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...

The regular hexagon is the regular polygon with six sides, as illustrated above. The inradius r, circumradius R, sagitta s, and area A of a regular hexagon can be computed ...

The rhombic triacontahedron is a zonohedron which is the dual polyhedron of the icosidodecahedron A_4 (Holden 1971, p. 55). It is Wenninger dual W_(12). It is composed of 30 ...

For a real positive t, the Riemann-Siegel Z function is defined by Z(t)=e^(itheta(t))zeta(1/2+it). (1) This function is sometimes also called the Hardy function or Hardy ...

Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards ...

The universal cover of a connected topological space X is a simply connected space Y with a map f:Y->X that is a covering map. If X is simply connected, i.e., has a trivial ...

The wallpaper groups are the 17 possible plane symmetry groups. They are commonly represented using Hermann-Mauguin-like symbols or in orbifold notation (Zwillinger 1995, p. ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...