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Let each of f(a,b,c) and g(a,b,c) be a triangle center function or the zero function, and let one of the following three conditions hold. 1. The degree of homogeneity of g ...

The interior of the triangle is the set of all points inside a triangle, i.e., the set of all points in the convex hull of the triangle's vertices. The simplest way to ...

A median triangle is a triangle whose sides are equal and parallel to the medians of a given triangle. The median triangle of the median triangle is similar to the given ...

Let the circles c_2 and c_3^' used in the construction of the Brocard points which are tangent to A_2A_3 at A_2 and A_3, respectively, meet again at D_A. The points D_AD_BD_C ...

The Euler triangle of a triangle DeltaABC is the triangle DeltaE_AE_BE_C whose vertices are the midpoints of the segments joining the orthocenter H with the respective ...

A scalene triangle is a triangle that has three unequal sides, such as those illustrated above.

The triangle space T is the set of triples (a,b,c) of real numbers that are side lengths of a (Euclidean) triangle, i.e., T={(a,b,c):0<a<b+c,0<b<c+a,0<c<a+b} (Kimberling ...

Clark's triangle is a number triangle created by setting the vertex equal to 0, filling one diagonal with 1s, the other diagonal with multiples of an integer f, and filling ...

The cyclocevian triangle DeltaA^('')B^('')C^('') of a reference triangle DeltaABC with respect to a point P is the triangle formed by the vertices determined by the ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...