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For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

The excentral triangle, also called the tritangent triangle, of a triangle DeltaABC is the triangle J=DeltaJ_AJ_BJ_C with vertices corresponding to the excenters of DeltaABC. ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

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 ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

A vertex-transitive graph, also sometimes called a node symmetric graph (Chiang and Chen 1995), is a graph such that every pair of vertices is equivalent under some element ...

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

In general, the external similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...