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The Tusi couple is a 2-cusped hypocycloid obtained by rolling a circle of radius a inside a circle of radius 2a. The result is a line segment (Steinhaus 1999, p. 145; Kanas ...

Let X be a connected topological space. Then X is unicoherent provided that for any closed connected subsets A and B of X, if X=A union B, then A intersection B is connected. ...

Given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, known as the Weill point, ...

The Yff contact triangle DeltaX_AX_BX_C (a term coined here for the first time), is the Cevian triangle of Kimberling center X_(190). It is the polar triangle of the Yff ...

A figure used in many Asian cultures to symbolize the unity of the two "opposite" female and male elements, the "yin" and "yang." The solid and hollow parts composing the ...

The de Longchamps line is central line L_(32) with trilinear equation a^3alpha+b^3beta+c^3gamma=0 (Droussent 1953; Kimberling 1998, p. 150) which is the anticomplement of the ...

Given a triangle DeltaABC, the triangle DeltaH_AH_BH_C whose vertices are endpoints of the altitudes from each of the vertices of DeltaABC is called the orthic triangle, or ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

It is always possible to "fairly" divide a cake among n people using only vertical cuts. Furthermore, it is possible to cut and divide a cake such that each person believes ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...