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The elliptic exponential function eexp_(a,b)(u) gives the value of x in the elliptic logarithm eln_(a,b)(x)=1/2int_infty^x(dt)/(sqrt(t^3+at^2+bt)) for a and b real such that ...

The envelope of a one-parameter family of curves given implicitly by U(x,y,c)=0, (1) or in parametric form by (f(t,c),g(t,c)), is a curve that touches every member of the ...

The center of an inner Soddy circle. It has equivalent triangle center functions alpha = 1+(2Delta)/(a(b+c-a)) (1) alpha = sec(1/2A)cos(1/2B)cos(1/2C)+1, (2) where Delta is ...

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

Let O and I be the circumcenter and incenter of a triangle with circumradius R and inradius r. Let d be the distance between O and I. Then d^2=R(R-2r) (Mackay 1886-1887; ...

Define A^' to be the point (other than the polygon vertex A) where the triangle median through A meets the circumcircle of ABC, and define B^' and C^' similarly. Then the ...

The far-out point F of a triangle DeltaABC is the inverse point of the triangle centroid with respect to the circumcircle of DeltaABC. For a triangle with side lengths a, b, ...

Four line geometry is a finite geometry subject to the following three axioms: 1. there exist exactly four lines, 2. any two distinct lines have exactly one point of on both ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

An isocubic is a triangle cubic that is invariant under an isoconjugation. Self-isogonal and self-isotomic cubics are examples of isocubics.