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Let A, B, and C be three circles in the plane, and let X be any circle touching B and C. Then build up a chain of circles such that Y:CAX, Z:ABY, X^':BCZ, Y^':CAX^', ...

Niven's theorem states that if x/pi and sinx are both rational, then the sine takes values 0, +/-1/2, and +/-1. Particular cases include sin(pi) = 0 (1) sin(pi/2) = 1 (2) ...

Given a triangle DeltaABC, construct the contact triangle DeltaDEF. Then the Nobbs points are the intersections of the corresponding sides of triangles DeltaABC and DeltaDEF, ...

A polyhedral graph having nine vertices. There are 2606 nonisomorphic nonahedral graphs, as first enumerated by Federico (1969; Duijvestijn and Federico 1981). Named ...

A knot which is not alternating. Unlike alternating knots, flype moves are not sufficient to pass between all minimal diagrams of a given nonalternating knot (Hoste et al. ...

Consider the number of sequences that can be formed from permutations of a set of elements such that each partial sum is nonnegative. The number of sequences with nonnegative ...

A numeral is a symbol used to represent a number. Arabic numerals (0-9) are the ones most commonly used today. Other types, mainly of historical interest, include Egyptian, ...

The Ochoa curve is the elliptic curve 3Y^2=2X^3+386X^2+256X-58195, given in Weierstrass form as y^2=x^3-440067x+106074110. The complete set of 23 integer solutions (where ...

A number which is simultaneously octagonal and square. Let O_n denote the nth octagonal number and S_m the mth square number, then a number which is both octagonal and square ...

The set of octonions, also sometimes called Cayley numbers and denoted O, consists of the elements in a Cayley algebra. A typical octonion is of the form ...