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The pedal curve of a unit circle with parametric equation x = cost (1) y = sint (2) with pedal point (x,y) is x_p = cost-ycostsint+xsin^2t (3) y_p = ...

Let a cone of opening parameter c and vertex at (0,0,0) intersect a sphere of radius r centered at (x_0,y_0,z_0), with the cone oriented such that its axis does not pass ...

Let E be a simply connected compact set in the complex plane. By the Riemann mapping theorem, there is a unique analytic function ...

The automorphism group Co_1 of the Leech lattice modulo a center of order two is called "the" Conway group. There are 15 exceptional conjugacy classes of the Conway group. ...

The cyclocevian triangle DeltaA^('')B^('')C^('') of a reference triangle DeltaABC with respect to a point P is the triangle formed by the vertices determined by the ...

The Darboux cubic Z(X_(20)) of a triangle DeltaABC is the locus of all pedal-cevian points (i.e., of all points whose pedal triangle is perspective with DeltaABC). It is a ...

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. ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

The center J_i of an excircle. There are three excenters for a given triangle, denoted J_1, J_2, J_3. The incenter I and excenters J_i of a triangle are an orthocentric ...

The first Morley adjunct triangle is the triangle DeltaA^('')B^('')C^('') illustrated above, where DeltaA^'B^'C^' is the first Morley triangle. Unlike the first Morley ...