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A method of determining the maximum number of positive and negative real roots of a polynomial. For positive roots, start with the sign of the coefficient of the lowest (or ...

The number of bases in which 1/p is a repeating decimal (actually, repeating b-ary) of length l is the same as the number of fractions 0/(p-1), 1/(p-1), ..., (p-2)/(p-1) ...

Thâbit ibn Kurrah's rules is a beautiful result of Thâbit ibn Kurrah dating back to the tenth century (Woepcke 1852; Escott 1946; Dickson 2005, pp. 5 and 39; Borho 1972). ...

A graph is said to be H^*-connected if it is either Hamilton-connected or Hamilton-laceable. S. Wagon (pers. comm., May. 20, 2013; Dupuis and Wagon 2014) conjecture that all ...

The rule (F,F=>G)/G, where => means "implies," which is the sole rule of inference in propositional calculus. This rule states that if each of F and F=>G is either an axiom ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

A sequential substitution system is a substitution system in which a string is scanned from left to right for the first occurrence of the first rule pattern. If the pattern ...

The Ricci flow equation is the evolution equation d/(dt)g_(ij)(t)=-2R_(ij) for a Riemannian metric g_(ij), where R_(ij) is the Ricci curvature tensor. Hamilton (1982) showed ...

A related rates problem is the determination of the rate at which a function defined in terms of other functions changes. Related rates problems can be solved by computing ...

A three-dimensional coordinate system in which the axes do not satisfy the right-hand rule.