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Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

The infimum is the greatest lower bound of a set S, defined as a quantity m such that no member of the set is less than m, but if epsilon is any positive quantity, however ...

A general integral transform is defined by g(alpha)=int_a^bf(t)K(alpha,t)dt, where K(alpha,t) is called the integral kernel of the transform.

The lemniscate functions arise in rectifying the arc length of the lemniscate. The lemniscate functions were first studied by Jakob Bernoulli and Giulio Fagnano. A historical ...

A monomial is a product of positive integer powers of a fixed set of variables (possibly) together with a coefficient, e.g., x, 3xy^2, or -2x^2y^3z. A monomial can also be ...

If isosceles triangles with apex angles 2kpi/n are erected on the sides of an arbitrary n-gon A_0, and if this process is repeated with the n-gon A_1 formed by the free ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

The supremum is the least upper bound of a set S, defined as a quantity M such that no member of the set exceeds M, but if epsilon is any positive quantity, however small, ...