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The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

The 34 distinct convergent hypergeometric series of order two enumerated by Horn (1931) and corrected by Borngässer (1933). There are 14 complete series for which ...

One of the three standard tori given by the parametric equations x = a(1+cosv)cosu (1) y = a(1+cosv)sinu (2) z = asinv, (3) corresponding to the torus with a=c. It has ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

An Archimedean spiral with polar equation r=a/theta. (1) The hyperbolic spiral, also called the inverse spiral (Whittaker 1944, p. 83), originated with Pierre Varignon in ...

The impossible fork (Seckel 2002, p. 151), also known as the devil's pitchfork (Singmaster), blivet, or poiuyt, is a classic impossible figure originally due to Schuster ...

The term "indeterminate" is sometimes used as a synonym for unknown or variable (Becker and Weispfenning 1993, p. 188). A mathematical expression can also be said to be ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

If the square is instead erected internally, their centers form a triangle DeltaI_AI_BI_C that has (exact) trilinear vertex matrix given by (1) (E. Weisstein, Apr. 25, 2004). ...