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Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

"Analysis of Variance." A statistical test for heterogeneity of means by analysis of group variances. ANOVA is implemented as ANOVA[data] in the Wolfram Language package ...

The term "Aristotle gap"' is introduced in this work to refer to the angle between the first and last member of a 5-tetrahedral ring. This gap has angle measure theta = ...

The partial differential equation u_t+u_x+uu_x-u_(xxt)=0 (Benjamin et al. 1972; Arvin and Goldstein 1985; Zwillinger 1997, p. 130). A generalized version is given by u_t-del ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

The cubitruncated cuboctahedron (called the cubotruncated cuboctahedron by Wenninger 1971, p. 121) is the uniform polyhedron with Maeder index 16 (Maeder 1997), Wenninger ...

The cubohemioctahedron is the uniform polyhedron with Maeder index 15 (Maeder 1997), Wenninger index 78 (Wenninger 1989), Coxeter index 51 (Coxeter et al. 1954), and Har'El ...

The ditrigonal dodecadodecahedron, also called the ditrigonal dodecahedron, is the uniform polyhedron with Maeder index 41 (Maeder 1997), Wenninger index 80 (Wenninger 1989), ...

A (general) dodecahedron is a polyhedron having 12 faces. Examples include the Bilinski dodecahedron, decagonal prism, elongated square dipyramid (Johnson solid J_(15)), ...