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The Simson cubic is the triangle cubic that is the locus of tripoles of the Simson lines of a triangle DeltaABC. It has trilinear equation ...

A small circle is a spheric section that does not contain a diameter of the sphere (Kern and Bland 1948, p. 87; Tietze 1965, p. 25).

The perspectrix X of a pair of paralogic triangles DeltaA_1A_2A_3 and DeltaB_1B_2B_3 bisects the line joining the two orthocenters H_A and H_B (Johnson 1929, p. 259).

Gardner showed how to dissect a square into eight and nine acute scalene triangles. W. Gosper discovered a dissection of a unit square into 10 acute isosceles triangles, ...

The Star of Lakshmi is the star figure {8/2}, that is used in Hinduism to symbolize Ashtalakshmi, the eight forms of wealth. This symbol appears prominently in the Lugash ...

A quadrilateral which has an incircle, i.e., one for which a single circle can be constructed which is tangent to all four sides. Opposite sides of such a quadrilateral ...

The center of the Taylor circle. It has triangle center function alpha_(389)=cosA-cos(2A)cos(B-C) and is Kimberling center X_(389), which is the center of the Spieker circle ...

Given rods of length 1, 2, ..., n, how many distinct triangles T(n) can be made? Lengths for which l_i>=l_j+l_k (1) obviously do not give triangles, but all other ...

A triangle line is a line with trilinear equation lalpha+mbeta+ngamma=0 defined relative to a reference triangle. A triangle line is called a central line iff l:m:n is a ...

The total power of a triangle is defined by P=1/2(a_1^2+a_2^2+a_3^2), (1) where a_i are the side lengths, and the "partial power" is defined by p_1=1/2(a_2^2+a_3^2-a_1^2). ...