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For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

A lion and a man in a closed arena have equal maximum speeds. What tactics should the lion employ to be sure of his meal? This problem was stated by Rado in 1925 (Littlewood ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

The eighth proposition in the third book of the Elements is one of Euclid's most complex propositions. It shows that a segment through an outside point D and a circle is ...

A group that coincides with its commutator subgroup. If G is a non-Abelian group, its commutator subgroup is a normal subgroup other than the trivial group. It follows that ...

A chart made by plotting the numeric values of a set of quantities as a set of adjacent circular wedges with arc lengths proportional to the total amount. All wedges taken ...

A sphere is defined as the set of all points in three-dimensional Euclidean space R^3 that are located at a distance r (the "radius") from a given point (the "center"). Twice ...

The combination of a central dilation and a rotation about the same center. However, the combination of a central dilation and a rotation whose centers are distinct is also a ...

The Stammler circle is the circumcircle of the Stammler triangle. Unexpectedly, it has center at the circumcenter O (X_3) of the reference triangle and radius 2R (Ehrmann and ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...