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The word configuration is sometimes used to describe a finite collection of points p=(p_1,...,p_n), p_i in R^d, where R^d is a Euclidean space. The term "configuration" also ...

Given two normal subgroups G_1 and G_2 of a group, and two normal subgroups H_1 and H_2 of G_1 and G_2 respectively, H_1(G_1 intersection H_2) is normal in H_1(G_1 ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

A coincidence is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection (Diaconis and Mosteller 1989). Given a large number ...

Like the entire harmonic series, the harmonic series sum_(k=1)^infty1/(p_k)=infty (1) taken over all primes p_k also diverges, as first shown by Euler in 1737 (Nagell 1951, ...

The complexity c_n of an integer n is the least number of 1s needed to represent it using only additions, multiplications, and parentheses. For example, the numbers 1 through ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...

The Stammler circles are the three circles (apart from the circumcircle), that intercept the sidelines of a reference triangle DeltaABC in chords of lengths equal to the ...

Bertelsen's number is an erroneous name erroneously given to the erroneous value of pi(10^9)=50847478, where pi(x) is the prime counting function. This value is 56 lower than ...