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The trilinear pole of the orthotransversal of a point P is called its orthocorrespondent. The orthocorrespondent of a point P=p:q:r is given by where S_A, S_B, and S_C is ...

Orthogonal circles are orthogonal curves, i.e., they cut one another at right angles. By the Pythagorean theorem, two circles of radii r_1 and r_2 whose centers are a ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...

A statement which appears self-contradictory or contrary to expectations, also known as an antinomy. Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent ...

Given any straight line and a point not on it, there "exists one and only one straight line which passes" through that point and never intersects the first line, no matter ...

A parallelian is a line drawn parallel to one side of a triangle. The three lines drawn through a given point are known as the triangle's parallelians. There exists a unique ...

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...

The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

The lines containing the three points of the intersection of the three pairs of opposite sides of a (not necessarily regular) hexagon. There are 6! (i.e., 6 factorial) ...

Inspired by computer simulations of fossilized worms trails published by Raup and Seilacher (1969), computer scientist Mike Paterson at the University of Warwick and ...