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The principal theorem of axonometry, first published without proof by Pohlke in 1860. It states that three segments of arbitrary length a^'x^', a^'y^', and a^'z^' which are ...

The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...

A transformation that preserves angles and changes all distances in the same ratio, called the ratio of magnification. A similarity can also be defined as a transformation ...

Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...

For a plane curve, the tangential angle phi is defined by rhodphi=ds, (1) where s is the arc length and rho is the radius of curvature. The tangential angle is therefore ...

A tesseral harmonic is a spherical harmonic of the form cos; sin(mphi)P_l^m(costheta). These harmonics are so named because the curves on which they vanish are l-m parallels ...

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 ...

A triple of three arbitrary vectors with common vertex (Altshiller-Court 1979), often called a trihedral angle since it determines three planes. The vectors are often taken ...

A curve which can be used to trisect an angle. Although an arbitrary angle cannot be trisected using only compass and straightedge (i.e., according to the strict rules of ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...