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The anticomplementary circle is the circumcircle of the anticomplementary triangle. It has radius R_A=2R, where R is the circumradius of the reference triangle, and center at ...

The centralizer of an element z of a group G is the set of elements of G which commute with z, C_G(z)={x in G,xz=zx}. Likewise, the centralizer of a subgroup H of a group G ...

The inverse curve of the circle with parametric equations x = acost (1) y = asint (2) with respect to an inversion circle with center (x,y) and radius R is given by x_i = ...

A transformation of the plane which transforms collinear points into collinear points. A projective collineation transforms every one-dimensional form projectively, and a ...

Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

Two similar figures with parallel homologous lines and connectors of homologous points concurrent at the homothetic center are said to be in homothetic position. If two ...

An n-dimensional open ball of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Explicitly, the open ball with center x ...

Two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 are orthologic if the perpendiculars from the vertices A_1, B_1, C_1 on the sides B_2C_2, A_2C_2, and A_2B_2 are concurrent. ...

The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...

The Plateau curves were studied by the Belgian physicist and mathematician Joseph Plateau. They have Cartesian equation x = (asin[(m+n)t])/(sin[(m-n)t]) (1) y = ...