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Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards ...

The unknot, also called the trivial knot (Rolfsen 1976, p. 51), is a closed loop that is not knotted. In the 1930s Reidemeister first proved that knots exist which are ...

An unordered factorization is a factorization of a number into a product of factors where order is ignored. The following table lists the unordered factorizations of the ...

A number v=xy with an even number n of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

A Wagstaff prime is a prime number of the form (2^p+1)/3 for p a prime number. The first few are given by p=3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, ...

The Wallis formula follows from the infinite product representation of the sine sinx=xproduct_(n=1)^infty(1-(x^2)/(pi^2n^2)). (1) Taking x=pi/2 gives ...