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A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

Any two ranges {ABC...} and {A^'B^'C^'...} which are situated on the same or different lines are said to be homographic when the cross ratio of any four points on one range ...

An integer kappa equal to 0 or 1 which vanishes iff the product manifold M^4×R can be given a smooth structure. Here, M^n is a compact connected topological four-manifold.

Four bits or half a byte, also sometimes spelled "nybble." Since a nibble encodes values from 0 to 2^4-1=15, it can conveniently be represented using a single hexadecimal ...

Given four points, A, B, C, and H, let H be the orthocenter of DeltaABC. Then A is the orthocenter DeltaHBC, B is the orthocenter of DeltaHAC, and C is the orthocenter of ...

The Pasch configuration is the unbalanced (6_2,4_3) configuration (since there are two lines through each of six points and three points on each of four lines) illustrated ...

A plane figure consisting of four points, each of which is joined to two other points by a line segment (where the line segments may intersect). A quadrangle may therefore be ...

A flexible polyhedron due to C. Schwabe (with the appearance of having four horns) which flexes from one totally flat configuration to another, passing through intermediate ...

A point where a curve intersects itself along four arcs. The above plot shows the quadruple point at the origin of the quadrifolium (x^2+y^2)^3-4x^2y^2=0.