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If equilateral triangles DeltaABE_(AB), DeltaBCE_(BC), and DeltaACE_(AC) are erected externally on the sides of any triangle DeltaABC, then their centers N_(AB), N_(BC), and ...

An extreme point of a subset K of a vector space X is an extreme set S of K which consists of a single point x in K. The collection of all extreme points of K is sometimes ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...

Let f:R×R->R be a one-parameter family of C^2 map satisfying f(0,0)=0 [(partialf)/(partialx)]_(mu=0,x=0)=0 [(partial^2f)/(partialx^2)]_(mu=0,x=0)>0 ...

A closed interval corresponding to a finite portion of an infinite line. Line segments are generally labeled with two letters corresponding to their endpoints, say A and B, ...

Consider a knot as being formed from two tangles. The following three operations are called mutations. 1. Cut the knot open along four points on each of the four strings ...

If P(x,y) and P(x^',y^') are two points on an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1, (1) with eccentric angles phi and phi^' such that tanphitanphi^'=b/a (2) and A=P(a,0) and ...

One of the eight convex deltahedra built up from 16 equilateral triangles. It consists of two oppositely faced square pyramids rotated 45 degrees to each other and separated ...