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The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

The orthojoin of a point X=l:m:n is defined as the orthopole of the corresponding trilinear line lalpha+mbeta+ngamma. In other words, the orthojoin of Kimberling center X_i ...

A hypersphere S^n is parallelizable if there are n vector fields that are linearly independent at each point. There exist only three parallelizable spheres: S^1, S^3, and S^7 ...

Let P=p:q:r and U=u:v:w be distinct points, neither lying on a side line of the reference triangle DeltaABC. Then the P-cross conjugate of U is the point ...

Let a homogeneous solid contain a convex hole K and take x-rays so that the "darkness" at each point on a photographic plate determines the length of the chord of K along the ...

Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called ...

Each centered convex body of sufficiently high dimension has an "almost spherical" k-dimensional central section.

A conic section on which the midpoints of the sides of any complete quadrangle lie. The three diagonal points P, Q, and R also lie on this conic.

A geometric implement discovered in a 19th century book, and whose inventor is unknown. It essentially consists of a semicircle, a segment SR which prolongs its diameter and ...