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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 maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

A Pólya plot is a plot of the vector field of (R[f(z)],-I[f(z)]) of a complex function f(z). Several examples are shown above. Pólya plots can be created in the Wolfram ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

Let sigma(m) be the divisor function of m. Then two numbers m and n are a quasiamicable pair if sigma(m)=sigma(n)=m+n+1. The first few are (48, 75), (140, 195), (1050, 1925), ...

A RAT-free ("right angle triangle-free") set is a set of points, no three of which determine a right triangle. Let f(n) be the largest integer such that a RAT-free subset of ...

A set S of integers is said to be recursive if there is a total recursive function f(x) such that f(x)=1 for x in S and f(x)=0 for x not in S. Any recursive set is also ...

A partial solution to the Erdős squarefree conjecture which states that the binomial coefficient (2n; n) is never squarefree for all sufficiently large n>=n_0. Sárkőzy (1985) ...

The second Fermat point X^' or F_2 (also known as the second isogonic center) can be constructed by drawing equilateral triangles on the inside of a given triangle and ...

The second Napoleon point N^', also called the inner Napoleon point, is the concurrence of lines drawn between polygon vertices of a given triangle DeltaABC and the opposite ...