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A hexagrammic prism is a prism formed by two regular hexagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c. The contraction of a prime ...

Every finite-dimensional Lie algebra of characteristic p!=0 has a faithful finite-dimensional representation.

The determinant of a knot is defined as |Delta(-1)|, where Delta(z) is the Alexander polynomial (Rolfsen 1976, p. 213).

Any finite semigroup is a divisor for an alternating wreath product of finite groups and semigroups.

The inverse curve of a lemniscate in a circle centered at the origin and touching the lemniscate where it crosses the x-axis produces a rectangular hyperbola (Wells 1991).

The surface of revolution generated by the external catenary between a fixed point a and its conjugate on the envelope of the catenary through the fixed point is equal in ...

Also known as the first fundamental form, ds^2=g_(ab)dx^adx^b. In the principal axis frame for three dimensions, ds^2=g_(11)(dx^1)^2+g_(22)(dx^2)^2+g_(33)(dx^3)^2. At ...

A logarithmic singularity is a singularity of an analytic function whose main z-dependent term is of order O(lnz). An example is the singularity of the Bessel function of the ...