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A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

The abundancy of a number n is defined as the ratio sigma(n)/n, where sigma(n) is the divisor function. For n=1, 2, ..., the first few values are 1, 3/2, 4/3, 7/4, 6/5, 2, ...

An axiom is a proposition regarded as self-evidently true without proof. The word "axiom" is a slightly archaic synonym for postulate. Compare conjecture or hypothesis, both ...

The longstanding conjecture that the nonimaginary solutions E_n of zeta(1/2+iE_n)=0, (1) where zeta(z) is the Riemann zeta function, are the eigenvalues of an "appropriate" ...

Given a set S with a subset E, the complement (denoted E^' or E^_) of E with respect to S is defined as E^'={F:F in S,F not in E}. (1) Using set difference notation, the ...

The dihedral angle is the angle theta between two planes. The dihedral angle between the planes a_1x+b_1y+c_1z+d_1 = 0 (1) a_2x+b_2y+c_2z+d_2 = 0 (2) which have normal ...

An (n,k) fountain is an arrangement of n coins in rows such that exactly k coins are in the bottom row and each coin in the (i+1)st row touches exactly two in the ith row. ...

The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the ...

Gibrat's distribution is a continuous distribution in which the logarithm of a variable x has a normal distribution, P(x)=1/(xsqrt(2pi))e^(-(lnx)^2/2), (1) defined over the ...