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A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

A board covered by a lattice of pegs around which one can span rubber bands to form segments and polygons. It was invented by the Egyptian mathematician and pedagogist Caleb ...

An attractive compound can be constructed of 6 pentagonal prisms having unit edge lengths, as illustrated above. A net for the solid is illustrated above, where s_1 = ...

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

Given a triangle, draw a Cevian to one of the bases that divides it into two triangles having congruent incircles. The positions and sizes of these two circumcircles can then ...

Consider a convex plane curve K with perimeter L, and the set of points P exterior to K. Further, let t_1 and t_2 be the perpendicular distances from P to K (with ...

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...