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A class of area-preserving maps of the form theta_(i+1) = theta_i+2pialpha(r_i) (1) r_(i+1) = r_i, (2) which maps circles into circles but with a twist resulting from the ...

A hyperbolic paraboloid is the quadratic and doubly ruled surface given by the Cartesian equation z=(y^2)/(b^2)-(x^2)/(a^2) (1) (left figure). An alternative form is z=xy (2) ...

Let A and B be two classes of positive integers. Let A(n) be the number of integers in A which are less than or equal to n, and let B(n) be the number of integers in B which ...

Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it ...

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

The area element for a surface with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2 is dA=sqrt(EG-F^2)du ^ dv, where du ^ dv is the wedge product.

As used in physics, the term "exact" generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, ...

For a form Q, the generic character chi_i(Q) of Q is defined as the values of chi_i(m) where (m,2d)=1 and Q represents m: chi_1(Q), chi_2(Q), ..., chi_r(Q) (Cohn 1980, p. ...

Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm. This method reduces the dividend and ...

A number of the form n^...^_()_(n)n, where Knuth up-arrow notation has been used. The first few Ackermann numbers are 1^1=1, 2^^2=4, and ...