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Relates evolutes to single paths in the calculus of variations. Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898. It states: "When a single ...

An n-cycle is a finite sequence of points Y_0, ..., Y_(n-1) such that, under a map G, Y_1 = G(Y_0) (1) Y_2 = G(Y_1) (2) Y_(n-1) = G(Y_(n-2)) (3) Y_0 = G(Y_(n-1)). (4) In ...

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

A figurate number in which layers of polygons are drawn centered about a point instead of with the point at a polygon vertex.

Discrepancy is a measure of the deviation of a point set from a uniform distribution. In general, the computation of the discrepancy of a point set is computationally ...

In elliptic n-space, the pole of an (n-1)-flat is a point located at an arc length of pi/2 radians away from each point of the (n-1)-flat.

The Galilean spiral is the curve with polar equation r=btheta^2-a for a>0 which describes the trajectory of a point uniformly accelerated along a line rotating about a point.

Mark a point P on a side of a triangle and draw the perpendiculars from the point to the two other sides. The line between the feet of these two perpendiculars is called the ...

An graph edge of a graph is separating if a path from a point A to a point B must pass over it. Separating graph edges can therefore be viewed as either bridges or dead ends.

The distance a point moves due to shear divided by the perpendicular distance of a point from the invariant line.