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Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

The use of the principle of mathematical induction in a proof. Induction used in mathematics is often called mathematical induction.

Let D be a subset of the nonnegative integers Z^* with the properties that (1) the integer 0 is in D and (2) any time that the interval [0,n] is contained in D, one can show ...

Strong convergence is the type of convergence usually associated with convergence of a sequence. More formally, a sequence {x_n} of vectors in a normed space (and, in ...

Pairs of primes of the form (p, p+4) are called cousin primes. The first few are (3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), ... (OEIS A023200 and ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

The randomization of a deck of cards by repeated interleaving. More generally, a shuffle is a rearrangement of the elements in an ordered list. Shuffling by exactly ...

11 11 1 11 2 2 11 2 4 2 11 3 6 6 3 11 3 9 10 9 3 11 4 12 19 19 12 4 11 4 16 28 38 28 16 4 11 5 20 44 66 66 44 20 5 11 5 25 60 110 126 110 60 25 5 1 (1) Losanitsch's triangle ...

There are several closely related results that are variously known as the binomial theorem depending on the source. Even more confusingly a number of these (and other) ...

11 21 3 41 4 7 81 5 11 15 161 6 16 26 31 32 (1) The number triangle illustrated above (OEIS A008949) composed of the partial sums of binomial coefficients, a_(nk) = ...