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A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The one-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the ...

A surface of revolution is a surface generated by rotating a two-dimensional curve about an axis. The resulting surface therefore always has azimuthal symmetry. Examples of ...

The nth order Bernstein expansion of a function f(x) in terms of a variable x is given by B_n(f,x)=sum_(j=0)^n(n; j)x^j(1-x)^(n-j)f(j/n), (1) (Gzyl and Palacios 1997, Mathé ...

Given a real number x, find the powers of a base b that will shift the digits of x a number of places n to the left. This is equivalent to solving b^x=b^nx (1) or x=n+log_bx. ...

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

Expressions of the form lim_(k->infty)x_0+sqrt(x_1+sqrt(x_2+sqrt(...+x_k))) (1) are called nested radicals. Herschfeld (1935) proved that a nested radical of real nonnegative ...

The AC method is an algorithm for factoring quadratic polynomials of the form p(x)=Ax^2+Bx+C with integer coefficients. As its name suggests, the crux of the algorithm is to ...

The above topological structure, composed of a countable union of compact sets, is called Alexander's horned sphere. It is homeomorphic with the ball B^3, and its boundary is ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...