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The Dou circle is the circle cutting the sidelines of the reference triangle DeltaABC at A^', A^(''), B^', B^(''), C^', and C^('') such that ...

The dual of a regular tessellation is formed by taking the center of each polygon as a vertex and joining the centers of adjacent polygons. The triangular and hexagonal ...

A principal vertex x_i of a simple polygon P is called an ear if the diagonal [x_(i-1),x_(i+1)] that bridges x_i lies entirely in P. Two ears x_i and x_j are said to overlap ...

The angle obtained by drawing the auxiliary circle of an ellipse with center O and focus F, and drawing a line perpendicular to the semimajor axis and intersecting it at A. ...

Consider a point P inside a reference triangle DeltaABC, construct line segments AP, BP, and CP. The Ehrmann congruent squares point is the unique point P such that three ...

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-, ...

The evolute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_e = (a^2-b^2)/acos^3t (3) y_e = (b^2-a^2)/bsin^3t. ...

The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P-Q)·(dP)/(dt)=0 (1) for ...

A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some ...

p is an equireciprocal point if, for every chord [x,y] of a curve C, p satisfies |x-p|^(-1)+|y-p|^(-1)=c for some constant c. The foci of an ellipse are equichordal points.