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The Stammler circles are the three circles (apart from the circumcircle), that intercept the sidelines of a reference triangle DeltaABC in chords of lengths equal to the ...

A famous perceptual illusion in which the brain switches between seeing a young girl and an old woman (or "wife" and "mother in law"). An anonymous German postcard from 1888 ...

The Bevan point V of a triangle DeltaABC is the circumcenter of the excentral triangle DeltaJ_AJ_BJ_C. It is named in honor of Benjamin Bevan, a relatively unknown Englishman ...

Let T be a central triangle and let U(T) be its unary cofactor triangle. Then T and U(T) are perspective, and their perspector is called the eigencenter of T. Let the A-, B-, ...

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

A 24-dimensional Euclidean lattice. An automorphism of the Leech lattice modulo a center of two leads to the Conway group Co_1. Stabilization of the one- and two-dimensional ...

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

The tangential triangle is the triangle DeltaT_AT_BT_C formed by the lines tangent to the circumcircle of a given triangle DeltaABC at its vertices. It is therefore antipedal ...

The Lucas tangents triangle (a term coined here for the first time) is the triangle DeltaT_AT_BT_C formed by the pairwise tangents of the Lucas circles of a given reference ...