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The pentagonal icositetrahedron is the 24-faced dual polyhedron of the snub cube A_7 and Wenninger dual W_(17). The mineral cuprite (Cu_2O) forms in pentagonal ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...

A region in a knot or link projection plane surrounded by a circle such that the knot or link crosses the circle exactly four times. Two tangles are equivalent if a sequence ...

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875). Truchet's ...

Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes ...

The regular heptagon is the seven-sided regular polygon illustrated above, which has Schläfli symbol {7}. According to Bankoff and Garfunkel (1973), "since the earliest days ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

The number two (2) is the second positive integer and the first prime number. It is even, and is the only even prime (the primes other than 2 are called the odd primes). The ...