Search Results for ""

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

A bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...

A minimal surface given by the parametric equations x(u,v) = u-sinucoshv (1) y(u,v) = 1-cosucoshv (2) z(u,v) = 4sin(1/2u)sinh(1/2v) (3) (Gray 1997), or x(r,phi) = ...

The corkscrew surface, sometimes also called the twisted sphere (Gray 1997, p. 477), is a surface obtained by extending a sphere along a diameter and then twisting. It can be ...

A curve of order n is generally determined by n(n+3)/2 points. So a conic section is determined by five points and a cubic curve should require nine. But the Maclaurin-Bézout ...

A cyclotomic field Q(zeta) is obtained by adjoining a primitive root of unity zeta, say zeta^n=1, to the rational numbers Q. Since zeta is primitive, zeta^k is also an nth ...

Let G be a group of group order h and D be a set of k elements of G. If the set of differences d_i-d_j contains every nonzero element of G exactly lambda times, then D is a ...

The elongated pentagonal orthobicupola is a convex equilateral solid that is Johnson solid J_(38). The unit elongated pentagonal orthobicupola has volume ...

A shuffle of a deck of cards obtained by successively exchanging the cards in position 1, 2, ..., n with cards in randomly chosen positions. For 4<=n<=17, the most frequent ...