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Two triangles DeltaABC and DeltaA^'B^'C^' are said to be perspective, or sometimes homologic, from a line if the extensions of their three pairs of corresponding sides meet ...

External (or positive) and internal (or negative) similarity points of two circles with centers C and C^' and radii r and r^' are the points E and I on the lines CC^' such ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

Three or more points P_1, P_2, P_3, ..., are said to be collinear if they lie on a single straight line L. A line on which points lie, especially if it is related to a ...

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

The operation of exchanging all points of a mathematical object with their mirror images (i.e., reflections in a mirror). Objects that do not change handedness under ...

Two points z and z^S in C^* are symmetric with respect to a circle or straight line L if all circles and straight lines passing through z and z^S are orthogonal to L. Möbius ...

The Robbins constant is the mean line segment length, i.e., the expected distance between two points chosen at random in cube line picking, namely Delta(3) = (1) = (2) = ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...