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The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

Tietze's graph is the cubic graph on 12 nodes and 18 edges illustrated above in a number of embeddings. It is implemented in the Wolfram Language as GraphData["TietzeGraph"]. ...

Analysis

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

The pure equation x^p=C of prime degree p is irreducible over a field when C is a number of the field but not the pth power of an element of the field. Jeffreys and Jeffreys ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

Fok (1946) and Hazewinkel (1988, p. 65) call v(z) = 1/2sqrt(pi)Ai(z) (1) w_1(z) = 2e^(ipi/6)v(omegaz) (2) w_2(z) = 2e^(-ipi/6)v(omega^(-1)z), (3) where Ai(z) is an Airy ...