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A cubic lattice is a lattice whose points lie at positions (x,y,z) in the Cartesian three-space, where x, y, and z are integers. The term is also used to refer to a regular ...

The theta series of a lattice is the generating function for the number of vectors with norm n in the lattice. Theta series for a number of lattices are implemented in the ...

A geometric construction done with a movable compass alone. All constructions possible with a compass and straightedge are possible with a movable compass alone, as was ...

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point ...

The anticomplement of a point P in a reference triangle DeltaABC is a point P^' satisfying the vector equation P^'G^->=2GP^->, (1) where G is the triangle centroid of ...

An n×n magic square for which every pair of numbers symmetrically opposite the center sum to n^2+1. The Lo Shu is associative but not panmagic. The numbers of associative ...

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...

A pair of identical plane regions (mirror symmetric about two perpendicular lines through the center) which can be stitched together to form a baseball (or tennis ball). A ...

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 line segment KO^_ joining the symmedian point K and circumcenter O of a given triangle. It is the diameter of the triangle's Brocard circle, and lies along the Brocard ...