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Consider a reference triangle DeltaABC with circumcenter O and orthocenter H, and let DeltaA^*B^*C^* be its reflection triangle. Then Musselman's theorem states that the ...

An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

Let L, M, and N be lines through A, B, C, respectively, parallel to the Euler line. Let L^' be the reflection of L in sideline BC, let M^' be the reflection of M in sideline ...

The pathwidth of a graph G, also called the interval thickness, vertex separation number, and node searching number, is one less than the size of the largest set in a path ...

Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through ...

A prime-distance graph is a distance graph with distance set given by the set of prime numbers.

A prime circle of order 2n is a free circular permutation of the numbers from 1 to 2n with adjacent pairs summing to a prime. The number of prime circles for n=1, 2, ..., are ...

Prince Rupert's cube is the largest cube that can be made to pass through a given cube. In other words, the cube having a side length equal to the side length of the largest ...

The radical circle of three given circles is the circle having center at the radical center of the three circles and is orthogonal to all of them. (A circle with center at ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...