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The equilateral cevian triangle point of a triangle is the unique point P such that the Cevian triangle of P is equilateral. This point is Kimberling center X_(370).

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

The Euler-Gergonne-Soddy circle, a term coined here for the first time, is the circumcircle of the Euler-Gergonne-Soddy triangle. Since the Euler-Gergonne-Soddy triangle is a ...

The term "Euler function" may be used to refer to any of several functions in number theory and the theory of special functions, including 1. the totient function phi(n), ...

For |z|<1, product_(k=1)^infty(1+z^k)=product_(k=1)^infty(1-z^(2k-1))^(-1). (1) Both of these have closed form representation 1/2(-1;z)_infty, (2) where (a;q)_infty is a ...

The Euler points are the midpoints E_A, E_B, E_C of the segments which join the vertices A, B, and C of a triangle DeltaABC and the orthocenter H. They are three of the nine ...

Define A^' to be the point (other than the polygon vertex A) where the triangle median through A meets the circumcircle of ABC, and define B^' and C^' similarly. Then the ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

A functor is said to be faithful if it is injective on maps. This does not necessarily imply injectivity on objects. For example, the forgetful functor from the category of ...

Euler (1738, 1753) considered the series s_a(x)=sum_(n=1)^infty[1/(1-a^n)product_(k=0)^(n-1)(1-xa^(-k))]. He showed that just like log_a(a^n)=n, s_a(a^n)=n for nonnegative ...