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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 ...

With n cuts of a torus of genus 1, the maximum number of pieces which can be obtained is N(n)=1/6(n^3+3n^2+8n). The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, ...

A number of the form Tt_n=((n+2; 2); 2)=1/8n(n+1)(n+2)(n+3) (Comtet 1974, Stanley 1999), where (n; k) is a binomial coefficient. The first few values are 3, 15, 45, 105, 210, ...

Oriented spheres in complex Euclidean three-space can be represented as lines in complex projective three-space ("Lie correspondence"), and the spheres may be thought of as ...

A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...