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The de Longchamps point L is the reflection of the orthocenter H about the circumcenter O of a triangle. It has triangle center function alpha=cosA-cosBcosC, (1) and is ...

Given a triangle DeltaABC, construct the contact triangle DeltaT_AT_BT_C. Now extend lines parallel to the sides of the contact triangle from the Gergonne point. These ...

The Lemoine ellipse is an inconic (that is always an ellipse) that has inconic parameters x:y:z=(2(b^2+c^2)-a^2)/(bc):(2(a^2+c^2)-b^2)/(ac): (2(a^2+b^2)-c^2)/(ab). (1) The ...

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...

Let DeltaA^'B^'C^' be the reflection of the orthic triangle of the reference triangle DeltaABC in the nine-point center. Then DeltaA^'B^'C^' and DeltaABC are in perspective, ...

A generalization of Turán's theorem to non-complete graphs.

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

A tree with a finite number of branches at each fork and with a finite number of leaves at the end of each branch is called a finitely branching tree. König's lemma states ...

The limit test, also sometimes known as the nth term test, says that if lima_n!=0 or this limit does not exist as n tends to infinity, then the series suma_n does not ...

A regression that is linear in the unknown parameters used in the fit. The most common form of linear regression is least squares fitting. Least squares fitting of lines and ...