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The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

The 6.1.2 equation A^6=B^6+C^6 (1) is a special case of Fermat's last theorem with n=6, and so has no solution. No 6.1.n solutions are known for n<=6 (Lander et al. 1967; Guy ...

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on ...

The term "isomorphic" means "having the same form" and is used in many branches of mathematics to identify mathematical objects which have the same structural properties. ...

Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional ...

Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are ...

The game of tic-tac-toe, also spelled ticktacktoe and also known as 3-in-a-row or "naughts and crosses," is a game in which players alternate placing pieces (typically Xs for ...

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

The n-dimensional Keller graph, sometimes denoted G_n (e.g., Debroni et al. 2011), can be defined on a vertex set of 4^n elements (m_1,...,m_n) where each m_i is 0, 1, 2, or ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...