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The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...

Let c_1, c_2, and c_3 be the circles through the vertices A_2 and A_3, A_1 and A_3, and A_1 and A_2, respectively, which intersect in the first Brocard point Omega. ...

The first strong law of small numbers (Gardner 1980, Guy 1988, 1990) states "There aren't enough small numbers to meet the many demands made of them." The second strong law ...

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

An n-trapezohedron, also called an antidipyramid, antibipyramid, or deltohedron (not to be confused with a deltahedron), is a solid composed of interleaved symmetric ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...

The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...