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If two perpendicular lines are drawn through the orthocenter H of any triangle, these lines intercept each side (or its extension) in two points (labeled P_(12), P_(12)^', ...

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of ordered individuals ...

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 ...

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...

Pre-Algebra

Given a circle, the apothem is the perpendicular distance r from the midpoint of a chord to the circle's center. It is also equal to the radius R minus the sagitta h, r=R-h. ...

If the cross ratio kappa of {AB,CD} satisfy kappa^2-kappa+1=0, (1) then the points are said to form a bivalent range, and {AB,CD}={AC,DB}={AD,BC}=kappa (2) ...

A convex set K is centro-symmetric, sometimes also called centrally symmetric, if it has a center p that bisects every chord of K through p.

The four medians of a tetrahedron concur in a point which divides each tetrahedron median in the ratio 1:3, the longer segment being on the side of the vertex of the ...

Two or more lines which intersect in a point are said to concur.