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The line R[s]=1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first ...

The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

A googol is a large number equal to 10^(10^2)=10^(100) (i.e., a 1 with 100 zeros following it). Written out explicitly, ...

A diagram lemma which states that the above commutative diagram of Abelian groups and group homomorphisms with exact rows gives rise to an exact sequence This commutative ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

The Church-Turing thesis (formerly commonly known simply as Church's thesis) says that any real-world computation can be translated into an equivalent computation involving a ...

A random number generator produced by iterating X_(n+1)=|100lnX_n (mod 1)| for a seed X_0=0.1. This simple generator passes the noise sphere test for randomness by showing no ...

The term "God's number" is sometimes given to the graph diameter of Rubik's graph, which is the minimum number of turns required to solve a Rubik's cube from an arbitrary ...

A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

A random partition of a number n is one of the P(n) possible partitions of n, where P(n) is the partition function P. A random partition can be given by RandomPartition[n] in ...