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The geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex (Honsberger 1995, p. 120) is called the Steiner ...

A line can be specified in trilinear coordinates by parameters (l,m,n) such that the trilinear coordinates alpha:beta:gamma obey lalpha+mbeta+ngamma=0. (1) The trilinear line ...

A trochoid is the locus of a point at a distance b from the center of a circle of radius a rolling on a fixed line. A trochoid has parametric equations x = aphi-bsinphi (1) y ...

Begin with the Yff central triangle and then parallel-displace the isoscelizers in such a way as to reduce the central triangle to a point while keeping the other three ...

Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

A rose curve, also called Grandi's rose or the multifolium, is a curve which has the shape of a petalled flower. This curve was named rhodonea by the Italian mathematician ...

The Simson line is the line containing the feet P_1, P_2, and P_3 of the perpendiculars from an arbitrary point P on the circumcircle of a triangle to the sides or their ...

An Archimedean spiral is a spiral with polar equation r=atheta^(1/n), (1) where r is the radial distance, theta is the polar angle, and n is a constant which determines how ...

An Archimedean spiral with polar equation r=a/theta. (1) The hyperbolic spiral, also called the inverse spiral (Whittaker 1944, p. 83), originated with Pierre Varignon in ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...