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Let sum_(k=1)^(infty)u_k be a series with positive terms, and let rho=lim_(k->infty)u_k^(1/k). 1. If rho<1, the series converges. 2. If rho>1 or rho=infty, the series ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

Rosser's rule states that every Gram block contains the expected number of roots, which appears to be true for computable Gram blocks. Rosser et al. (1969) expressed a belief ...

For algebraic alpha |alpha-p/q|<1/(q^(2+epsilon)), with epsilon>0, has finitely many solutions. Klaus Roth received a Fields medal for this result.

If n>19, there exists a Poulet number between n and n^2. The theorem was proved in 1965.

A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux ...

A polyhedron consisting of a n-gon, a parallel 2n-gon rotated a half-edge turn, and a band of paired triangles separated by pentagons. The only true member giving a ...

Given two functions f and g analytic in A with gamma a simple loop homotopic to a point in A, if |g(z)|<|f(z)| for all z on gamma, then f and f+g have the same number of ...

A rounded rectangle is the shape obtained by taking the convex hull of four equal circles of radius r and placing their centers at the four corners of a rectangle with side ...

The process of approximating a quantity, be it for convenience or, as in the case of numerical computations, of necessity. If rounding is performed on each of a series of ...