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Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

Consider the sample standard deviation s=sqrt(1/Nsum_(i=1)^N(x_i-x^_)^2) (1) for n samples taken from a population with a normal distribution. The distribution of s is then ...

In general, an unresolved nth root, commonly involving a radical symbol RadicalBox[x, n], is known as a surd. However, the term surd or "surd expression" (e.g., Hardy 1967, ...

Abstractly, the tensor direct product is the same as the vector space tensor product. However, it reflects an approach toward calculation using coordinates, and indices in ...

In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols. In algebra, a term is a product of the form x^n (in the ...

One of the numbers 1, 2, 3, ... (OEIS A000027), also called the counting numbers or natural numbers. 0 is sometimes included in the list of "whole" numbers (Bourbaki 1968, ...

The crossed trough is the surface z=x^2y^2. (1) The coefficients of its first fundamental form are E = 1+4x^2y^4 (2) F = 4x^3y^3 (3) G = 1+4x^4y^2 (4) and of the second ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

The common logarithm is the logarithm to base 10. The notation logx is used by physicists, engineers, and calculator keypads to denote the common logarithm. However, ...

Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...