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J. Tupper concocted the amazing formula 1/2<|_mod(|_y/(17)_|2^(-17|_x_|-mod(|_y_|,17)),2)_|, where |_x_| is the floor function and mod(b,m) is the mod function, which, when ...

Vorobiev's theorem states that if F_l^2|F_k, then F_l|k, where F_n is a Fibonacci number and a|b means a divides b. The theorem was discovered by Vorobiev in 1942, but not ...

The x-axis is the horizontal axis of a two-dimensional plot in Cartesian coordinates that is conventionally oriented to point to the right (left figure). In three dimensions, ...

Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

Connect-Four is a tic-tac-toe-like two-player game in which players alternately place pieces on a vertical board 7 columns across and 6 rows high. Each player uses pieces of ...

A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, ...

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...

The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...