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According to G. Pólya, the method of finding geometric objects by intersection. 1. For example, the centers of all circles tangent to a straight line s at a given point P lie ...

A prime circle of order 2n is a free circular permutation of the numbers from 1 to 2n with adjacent pairs summing to a prime. The number of prime circles for n=1, 2, ..., are ...

A rounded rectangle is the shape obtained by taking the convex hull of four equal circles of radius r and placing their centers at the four corners of a rectangle with side ...

The triangle DeltaN_1N_2N_3 formed by joining a set of three Neuberg centers (i.e., centers of the Neuberg circles) obtained from the edges of a given triangle DeltaA_1A_2A_3 ...

The locus of the similitude center of two circles.

A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

The point at which the three lines connecting the vertices of two perspective triangles concur, sometimes also called the perspective center, homology center, or pole. In the ...

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 ...