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On a Riemannian manifold M, tangent vectors can be moved along a path by parallel transport, which preserves vector addition and scalar multiplication. So a closed loop at a ...

The mean line segment length l^_ is the average length of a line segment in line segment picking within some given shape. As summarized in the following table (where Delta(3) ...

The angular twist theta of a shaft with given cross section is given by theta=(TL)/(KG) (1) (Roark 1954, p. 174), where T is the twisting moment (commonly measured in units ...

Chebyshev iteration is a method for solving nonsymmetric problems (Golub and van Loan 1996, §10.1.5; Varga, 1962, Ch. 5). Chebyshev iteration avoids the computation of inner ...

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 ...

Adams' method is a numerical method for solving linear first-order ordinary differential equations of the form (dy)/(dx)=f(x,y). (1) Let h=x_(n+1)-x_n (2) be the step ...

The area of a surface or lamina is the amount of material needed to "cover" it completely. The area of a surface or collection of surfaces bounding a solid is called, not ...

Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, ...

Let E_n(f) be the error of the best uniform approximation to a real function f(x) on the interval [-1,1] by real polynomials of degree at most n. If alpha(x)=|x|, (1) then ...

The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...