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A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...

A plot of a function expressed in polar coordinates, with radius r as a function of angle theta. Polar plots can be drawn in the Wolfram Language using PolarPlot[r, {t, tmin, ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

A quasiregular polyhedron is the solid region interior to two dual regular polyhedra with Schläfli symbols {p,q} and {q,p}. Quasiregular polyhedra are denoted using a ...

Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These ...

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875). Truchet's ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

The de Longchamps point L is the reflection of the orthocenter H about the circumcenter O of a triangle. It has triangle center function alpha=cosA-cosBcosC, (1) and is ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...