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If a points A^', B^', and C^' are marked on each side of a triangle DeltaABC, one on each side (or on a side's extension), then the three Miquel circles (each through a ...

There are at least 15 classes of convex pentagonal tilings, as illustrated above. The first five were discovered during investigations of German mathematician Karl Reinhardt ...

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

Synergetics coordinates are a set of triangular coordinates in their plane (or their generalization to tetrahedral coordinates in space, or the analogs in higher dimensions). ...

The conjecture that, for any triangle, 8omega^3<ABC (1) where A, B, and C are the vertex angles of the triangle and omega is the Brocard angle. The Abi-Khuzam inequality ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

Dürer's solid, also known as the truncated triangular trapezohedron, is the 8-faced solid depicted in an engraving entitled Melencolia I by Albrecht Dürer (The British ...