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Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

The trilinear pole of the orthotransversal of a point P is called its orthocorrespondent. The orthocorrespondent of a point P=p:q:r is given by where S_A, S_B, and S_C is ...

The permanent is an analog of a determinant where all the signs in the expansion by minors are taken as positive. The permanent of a matrix A is the coefficient of x_1...x_n ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...

A set of 15 open problems on Schrödinger operators proposed by mathematical physicist Barry Simon (2000). This set of problems follows up a 1984 list of open problems in ...

There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...

The triangle line that passes through the inner and outer Soddy centers S and S^'. The Soddy line is central line L_(657) and has trilinear equation ...

Somos's quadratic recurrence constant is defined via the sequence g_n=ng_(n-1)^2 (1) with g_0=1. This has closed-form solution ...