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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 ...

For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. Although the algorithm ...

The parachute graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["ParachuteGraph"].

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 parapluie (French for 'umbrella') graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["ParapluieGraph"].

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) ...