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Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Then A is said to be alternative if, for all x,y in A, (x·y)·y=x·(y·y) (3) ...

An impossible hexnut modeled after the impossible torus. The figure above shows three impossible figures: the ambihelical hexnut in the lower left-hand corner, tribox in the ...

An archaic name for the torus.

A hyperbolic linear map R^n->R^n with integer entries in the transformation matrix and determinant +/-1 is an Anosov diffeomorphism of the n-torus, called an Anosov ...

Construct a chain C of 2n components in a solid torus V. Now thicken each component of C slightly to form a chain C_1 of 2n solid tori in V, where pi_1(V-C_1)=pi_1(V-C) via ...

A square matrix is called bisymmetric if it is both centrosymmetric and either symmetric or antisymmetric (Muir 1960, p. 19).

Let K_1 be a torus knot. Then the satellite knot with companion knot K_2 is a cable knot on K_2.

A canonical brick is a 1×2×4 cuboid.

A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.

Every compact 3-manifold is the connected sum of a unique collection of prime 3-manifolds.