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The orthojoin of a point X=l:m:n is defined as the orthopole of the corresponding trilinear line lalpha+mbeta+ngamma. In other words, the orthojoin of Kimberling center X_i ...

An orthonormal set is a set of normalized orthogonal vectors or functions.

The orthopoles of a line l with respect to the four triangles formed by three out of four vertices of any quadrilateral ABCD lie on a straight line L known as the orthopolar ...

An isoptic curve formed from the locus of tangents meeting at right angles. The orthoptic of a parabola is its conic section directrix. The orthoptic of a central conic was ...

The prescription that a trigonometry identity can be converted to an analogous identity for hyperbolic functions by expanding, exchanging trigonometric functions with their ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} ...

Given a set X, a set function mu^*:2^X->[0,infty] is said to be an outer measure provided that mu^*(emptyset)=0 and that mu^* is countably monotone, where emptyset is the ...

The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

Let A^' be the outermost vertex of the regular pentagon erected outward on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...