Titlebook: Why Prove it Again?; Alternative Proofs i John W. Dawson, Jr. Book 2015 Springer International Publishing Switzerland 2015 Alternative Proo

Euphonious

The Fundamental Theorem of Algebra,ed to alternative proof strategies, and we can analyze why the proof given by Gauss in his 1799 inaugural dissertation was the first to be accorded general acceptance, though it too would later be deemed not fully rigorous.

RUPT

as opposed to the formal notion of proof in mathematical log.This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new

Living-Will

The Pythagorean Theorem,known formulation concerning arbitrary ‘figures’ described on the sides of a right triangle. The first of those demonstrations is based on a comparison of areas and the second on similarity theory, a basic distinction that can be used as a first step in classifying many other proofs of the theorem as well.

PANIC

The Fundamental Theorem of Arithmetic,rts: First, every integer greater than 1 . a factorization into primes; second, any two factorizations of an integer greater than 1 into primes must be identical except for the order of the factors. The proofs of each of those parts will thus be considered separately.

大漩渦

The Infinitude of the Primes,rces, including many by eminent number theorists, that either erroneously describe the structure of Euclid’s proof or make false historical claims about it. It is wise, therefore, to begin by quoting Euclid’s argument directly, as it is given in Heath’s translation (Heath?., vol.?II, p.?412).

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