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An equilateral polygon is a polygon whose edges are all of equal length (Williams 1979, pp. 31-32). The most prominent examples of equilateral polygons are the regular ...

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.

Also known as the difference of squares method. It was first used by Fermat and improved by Gauss. Gauss looked for integers x and y satisfying y^2=x^2-N (mod E) for various ...

If the tangents at B and C to the circumcircle of a triangle DeltaABC intersect in a point K_1, then the circle with center K_1 and which passes through B and C is called the ...

Given T an unbiased estimator of theta so that <T>=theta. Then var(T)>=1/(Nint_(-infty)^infty[(partial(lnf))/(partialtheta)]^2fdx), where var is the variance.

Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

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 ...