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By analogy with the geometric centroid, the centroid of an arbitrary function f(x) is defined as <x>=(intxf(x)dx)/(intf(x)dx), (1) where the integrals are taken over the ...

Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

The geometric span is largest possible distance between two points drawn from a finite set of points. It is therefore closely related to the generalized diameter of a closed ...

Assignment of each graph edge of a graph to one of two color classes (commonly designation "red" and "green").

The dual of the uniform great rhombicuboctahedron and Wenninger dual W_(85).

Johnson solid J_(22).

Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy (ace)/(bdf)=1 (Honsberger 1995).

A function which satisfies f(tx,ty)=t^nf(x,y) for a fixed n. Means, the Weierstrass elliptic function, and triangle center functions are homogeneous functions. A ...