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A hypergeometric identity discovered by Ramanujan around 1910. From Hardy (1999, pp. 13 and 102-103), (1) where a^((n))=a(a+1)...(a+n-1) (2) is the rising factorial (a.k.a. ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...

The Stammler circles are the three circles (apart from the circumcircle), that intercept the sidelines of a reference triangle DeltaABC in chords of lengths equal to the ...

The isogonal conjugate X^(-1) of a point X in the plane of the triangle DeltaABC is constructed by reflecting the lines AX, BX, and CX about the angle bisectors at A, B, and ...

If r experiments are performed with n_i possible outcomes for each experiment i=1,2,...,r, then there are a total of product_(i=1)^(r)n_i possible outcomes.

One out of a set of identical observations in a given experiment under identical conditions.

The nine-point center N (sometimes instead denoted F) is the center of the nine-point circle. It has equivalent triangle center functions alpha_5 = cos(B-C) (1) alpha_5 = ...

A dependent variable is a variable whose value depends on the values of one or more other independent variables. This notion comes up regularly in a variety of contexts. In ...

A variate is a generalization of the concept of a random variable that is defined without reference to a particular type of probabilistic experiment. It is defined as the set ...

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...