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A strange loop is a phenomenon in which, whenever movement is made upwards or downwards through the levels of some hierarchical system, the system unexpectedly arrives back ...

An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformations (such as rotation, reflection, inversion, or more ...

P. G. Tait undertook a study of knots in response to Kelvin's conjecture that the atoms were composed of knotted vortex tubes of ether (Thomson 1869). He categorized knots in ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series, Taylor's theorem (without the remainder term) was devised by ...

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...

In general, a tetrakis hexahedron is a non-regular icositetrahedron that can be constructed as a positive augmentation of a cube. Such a solid is also known as a ...

In the 1980s, Samuel Yates defined a titanic prime to be a prime number of at least 1000 decimal digits. The smallest titanic prime is 10^(999)+7. As of 1990, more than 1400 ...

A toroidal polyhedron is a polyhedron with genus g>=1 (i.e., one having one or more holes). Examples of toroidal polyhedra include the Császár polyhedron and Szilassi ...

In general, a triakis tetrahedron is a non-regular dodecahedron that can be constructed as a positive augmentation of a regular tetrahedron. Such a solid is also known as a ...