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The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspective axis or homology ...

The locus of the centers of all circumconics that also pass through the orthocenter of a triangle (which, when not degenerate, are rectangular hyperbolas) is a circle through ...

The Johnson triangle DeltaJ_AJ_BJ_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix ...

Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These ...

Given a point P and a triangle DeltaABC, the Cevian triangle DeltaA^'B^'C^' is defined as the triangle composed of the endpoints of the cevians though the Cevian point P. A ...

The Steiner circumellipse is the circumellipse that is the isotomic conjugate of the line at infinity and the isogonal conjugate of the Lemoine axis. It has circumconic ...

A Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...