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A function giving the distribution of the interpoint distances of a curve. It is defined by p(r)=1/Nsum_(ij)delta_(r_(ij)=r).

Pick a point O in the interior of a quadrilateral which is not a parallelogram. Join this point to each of the four vertices, then the locus of points O for which the sum of ...

A level set in three dimensions.

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

The inverse curve of the lituus is an Archimedean spiral with m=2, which is Fermat's spiral.

The catacaustic of a logarithmic spiral, where the origin is taken as the radiant point, is another logarithmic spiral. For an original spiral with parametric equations x = ...

The inverse curve of the logarithmic spiral r=e^(atheta) with inversion center at the origin and inversion radius k is the logarithmic spiral r=ke^(-atheta).

The pedal curve of a logarithmic spiral with parametric equation f = e^(at)cost (1) g = e^(at)sint (2) for a pedal point at the pole is an identical logarithmic spiral x = ...

The radial curve of the logarithmic spiral is another logarithmic spiral.

An equilateral parallelogram whose acute angles are 45 degrees. Sometimes, the restriction to 45 degrees is dropped, and it is required only that two opposite angles are ...