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Folkman's theorem is a theorem in mathematics, and more particularly in arithmetic combinatorics and Ramsey theory. According to this theorem, whenever the natural numbers are partitioned into finitely many subsets, there exist arbitrarily large sets of numbers all of whose sums belong to the same subset of the partition. The theorem had been discovered and proved independently by several mathematicians, before it was named "Folkman's theorem", as a memorial to Jon Folkman, by Graham, Rothschild, and Spencer. The integer version can be deduced from the set version by considering colourings which depend only on the number of 1s of the string. The integer version can also be deduced from Rado's theorem . The set version can be deduced from the integer version by using Ramsey's Theorem to restrict to a coloring which depends only on the cardinality of a set. The set version of this theorem can be deduced from Hindman's theorem . The higher k ge...

Rhetoric is a term that is broadly used, but its most classical definition is the art of persuasion. If you are asked to write a rhetorical analysis, you are really being asked to identify the particular strategies that an author is using to appeal to or persuade a given audience. In rhetoric, chiasmus or, less commonly, chiasm is a "reversal of grammatical structures in successive phrases or clauses – but no repetition of words". Chiasmus is a rhetorical device in which two or more clauses are balanced against each other by the reversal of their structures in order to produce an artistic effect. A popular chiasmus is " Never Let a Fool Kiss You or a Kiss Fool you". A literary device as the rhetoric of chiasmus may be expressed in the school of Physics as Chirality . In geometry, a kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch a common unit sphere. For a lattice packing the kissin...

Van der Waerden's theorem states that for any positive integers r and k there exists a positive integer N such that if the integers {1, 2, ..., N } are colored, each with one of r different colors, then there are at least k integers in arithmetic progression all of the same color. The smallest such N is the van der Waerden number W ( r , k ). As follow up from the article Heuristic lumped Stirling of mathematics, cardinality, induction, and the axiom of choice at Hilbert's paradox of the Grand Hotel   Combat Naps - Success Early On Three Laws, Four Basic Forces and Four types of bonds Van der Waerden test: Named after the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that k population distribution functions are equal. The Van der Waerden test converts the ranks from a standard Kruskal-Wallis one-way analysis of variance to quantiles of the standard normal distribution (details given below). T...