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There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x and ...

An algorithm for finding integer relations whose running time is bounded by a polynomial in the number of real variables (Ferguson and Bailey 1992). Unfortunately, it is ...

A geometric theorem related to the pentagram and also called the Pratt-kasapi theorem. It states ...

The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

A point process N on R is said to be interval stationary if for every r=1,2,3,... and for all integers i_i,...,i_r, the joint distribution of {tau_(i_1+k),...,tau_(i_r+k)} ...

A bijective map between two metric spaces that preserves distances, i.e., d(f(x),f(y))=d(x,y), where f is the map and d(a,b) is the distance function. Isometries are ...

A maltitude ("midpoint altitude") is a perpendicular drawn to a side of a quadrilateral from the midpoint M_i of the opposite side. If the quadrilateral is cyclic, then the ...

For triangles in the plane, AD·BE·CF=BD·CE·AF. (1) For spherical triangles, sinAD·sinBE·sinCF=sinBD·sinCE·sinAF. (2) This can be generalized to n-gons P=[V_1,...,V_n], where ...

For a triangle DeltaABC and three points A^', B^', and C^', one on each of its sides, the three Miquel circles are the circles passing through each polygon vertex and its ...

Given a point P and a triangle DeltaABC, the Miquel triangle is the triangle DeltaP_AP_BP_C connecting the side points P_A, P_B, and P_C of DeltaABC with respect to which M ...