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If the vertices A, B, and C of triangle DeltaABC lie on sides QR, RP, and PQ of the triangle DeltaPQR, then the three circumcircles CBP, ACQ, and BAR have a common point X. ...

Given two functions f and g analytic in A with gamma a simple loop homotopic to a point in A, if |g(z)|<|f(z)| for all z on gamma, then f and f+g have the same number of ...

The Steiner circle is the central circle with center at the nine-point center X_5 and radius R_S=3/2R, where R is the circumradius of the reference triangle. It is the ...

For a given point lattice, some number of points will be within distance d of the origin. A Waterman polyhedron is the convex hull of these points. A progression of Waterman ...

Two points P,Q on a compact Riemann surface such that P lies on every geodesic passing through Q, and conversely. An oriented surface where every point belongs to a ...

Fano's geometry is a finite geometry attributed to Fano from around the year 1892. This geometry comes with five axioms, namely: 1. There exists at least one line. 2. Every ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

C_4 is one of the two groups of group order 4. Like C_2×C_2, it is Abelian, but unlike C_2×C_2, it is a cyclic. Examples include the point groups C_4 (note that the same ...