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The 57-cell, also called the pentacontaheptachoron, is a regular self-dual locally projective polytope with 57 hemidodecahedral facets described by Coxeter (1982) and also ...

The coordinate system obtained by inversion of Cartesian coordinates, with u,v,w in (-infty,infty). The transformation equations are x = u/(u^2+v^2+w^2) (1) y = ...

The second Mersenne prime M_3=2^3-1, which is itself the exponent of Mersenne prime M_7=2^7-1=127. It gives rise to the perfect number P_7=M_7·2^6=8128. It is a Gaussian ...

The ABC (atom-bond connectivity) matrix A_(ABC) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt((d_i+d_j-2)/(d_id_j)), (1) where d_i are the ...

The ABC (atom-bond connectivity) spectral radius rho_(ABC) of a graph is defined as the largest eigenvalue of its ABC matrix. Chen (2019) showed that for a tree on 3 or more ...

Specifying two adjacent side lengths a and c of a triangle (with a<c) and one acute angle A opposite a does not, in general, uniquely determine a triangle. If sinA<a/c, there ...

The Abel-Plana formula gives an expression for the difference between a discrete sum and the corresponding integral. The formula can be derived from the argument principle ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

An Abelian semigroup is a set whose elements are related by a binary operation (such as addition, rotation, etc.) that is closed, associative, and commutative. A mathematical ...

An Abelian variety is an algebraic group which is a complete algebraic variety. An Abelian variety of dimension 1 is an elliptic curve.