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Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. Apéry (1979) proved that zeta(3) is irrational, although ...

The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

The points of intersection of the adjacent angle trisectors of the angles of any triangle DeltaABC are the polygon vertices of an equilateral triangle DeltaDEF known as the ...

The Soifer graph, illustrated above in a number of embeddings, is a planar graph on 9 nodes that tangles the Kempe chains in Kempe's algorithm and thus provides an example of ...

Zarankiewicz's conjecture asserts that graph crossing number for a complete bipartite graph K_(m,n) is Z(m,n)=|_n/2_||_(n-1)/2_||_m/2_||_(m-1)/2_|, (1) where |_x_| is the ...

Given an arithmetic progression of terms an+b, for n=1, 2, ..., the series contains an infinite number of primes if a and b are relatively prime, i.e., (a,b)=1. This result ...

Bezdek and Kuperberg (1991) have constructed packings of identical ellipsoids of densities arbitrarily close to ((24sqrt(2)-6sqrt(3)-2pi)pi)/(72)=0.753355... (OEIS A093824), ...

Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique ...

The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...