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The Chebyshev polynomials of the first kind are a set of orthogonal polynomials defined as the solutions to the Chebyshev differential equation and denoted T_n(x). They are ...

The decimal expansion of a number is its representation in base-10 (i.e., in the decimal system). In this system, each "decimal place" consists of a digit 0-9 arranged such ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

An arc-transitive graph, sometimes also called a flag-transitive graph, is a graph whose graph automorphism group acts transitively on its graph arcs (Godsil and Royle 2001, ...

In antiquity, geometric constructions of figures and lengths were restricted to the use of only a straightedge and compass (or in Plato's case, a compass only; a technique ...

Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

An n-digit number that is the sum of the nth powers of its digits is called an n-narcissistic number. It is also sometimes known as an Armstrong number, perfect digital ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...