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There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

The gyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating one of the pentagonal cupolas of a small rhombicosidodecahedron by 1/10 of a turn. It is ...

The metabigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating two of the pentagonal cupolas of a small rhombicosidodecahedron located in the ...

The metabigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating two of the pentagonal cupolas of a small rhombicosidodecahedron located in the ...

The trigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating three of the pentagonal cupolas of a small rhombicosidodecahedron by 1/10 of a turn ...

The rhombic dodecahedral graph is the Archimedean dual graph which is the skeleton of the rhombic dodecahedron (as well as the Bilinski dodecahedron). It is the Levi graph of ...

The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the ...

Cauchy's functional equation is the equation f(x+y)=f(x)+f(y). It was proved by Cauchy in 1821 that the only continuous solutions of this functional equation from R into R ...

A subset E of a topological space S is said to be of first category in S if E can be written as the countable union of subsets which are nowhere dense in S, i.e., if E is ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...