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A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

Let s_i be the sum of the products of distinct polynomial roots r_j of the polynomial equation of degree n a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the roots are taken ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

In this work, the name Pythagoras's constant will be given to the square root of 2, sqrt(2)=1.4142135623... (1) (OEIS A002193), which the Pythagoreans proved to be ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that every number ...