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The intersection H of the three altitudes AH_A, BH_B, and CH_C of a triangle is called the orthocenter. The name was invented by Besant and Ferrers in 1865 while walking on a ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...

There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

The Tucker circles are a generalization of the cosine circle and first Lemoine circle which can be viewed as a family of circles obtained by parallel displacing sides of the ...

The Zermelo-Fraenkel axioms are the basis for Zermelo-Fraenkel set theory. In the following (Jech 1997, p. 1), exists stands for exists, forall means for all, in stands for ...

Pre-Algebra

The Akhmim wooden tablet, often called the Cairo wooden tablet, is a document dating to 2000 BC, near the beginning of the Egyptian Middle Kingdom. It is housed in the Egypt ...

The (interior) bisector of an angle, also called the internal angle bisector (Kimberling 1998, pp. 11-12), is the line or line segment that divides the angle into two equal ...