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Two lines PQ and RS are said to be antiparallel with respect to the sides of an angle A if they make the same angle in the opposite senses with the bisector of that angle. If ...

The Clebsch diagonal cubic is a cubic algebraic surface given by the equation x_0^3+x_1^3+x_2^3+x_3^3+x_4^3=0, (1) with the added constraint x_0+x_1+x_2+x_3+x_4=0. (2) The ...

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 class of curve known as Dürer's conchoid appears in Dürer's work Instruction in Measurement with Compasses and Straight Edge (1525) and arose in investigations of ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the B- and C-excircles (with centers J_B and J_C, respectively). Of these, three correspond to the ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the incircle (with center I) and the A-excircle (with center J_A). Of these, three correspond to the ...

There are at least two distinct notions of linear space throughout mathematics. The term linear space is most commonly used within functional analysis as a synonym of 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 ...

A Steiner system S(t,k,v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...