Fermat’s last theorem: an alternative Pythagorean perspective
نویسندگان
چکیده
منابع مشابه
Note on an n-dimensional Pythagorean theorem
A famous theorem in Euclidean geometry often attributed to the Greek thinker Pythagoras of Samos (6th century, B.C.) states that if one of the angles of a planar triangle is a right angle, then the square of the length of the side opposite the right angle equals the sum of the squares of the lengths of the sides which form the right angle. There are less commonly known higherdimensional version...
متن کاملExponents 3 and 4 of Fermat’s Last Theorem and the Parametrisation of Pythagorean Triples
This document gives a formal proof of the cases n = 3 and n = 4 (and all their multiples) of Fermat’s Last Theorem: if n > 2 then for all integers x, y, z: x + y = z =⇒ xyz = 0. Both proofs only use facts about the integers and are developed along the lines of the standard proofs (see, for example, sections 1 and 2 of the book by Edwards [Edw77]). First, the framework of ‘infinite descent’ is b...
متن کاملThe Pythagorean Theorem: I. The finite case.
The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theorem as the basic result of noncommutative, metric, Euclidean Geometry. The emphasis in the present article is finite dimensionality, both "discrete" and "continuous."
متن کاملAbstract Pythagorean Theorem and Corresponding Functional Equations
PYTHAGOREAN THEOREM AND CORRESPONDING FUNCTIONAL EQUATIONS
متن کاملThe Pythagorean Theorem: What Is It About?
Although twenty five centuries old, the Pythagorean theorem appears vigorous and ubiquitous. A key to the distance formula in Descartes’s method of coordinates, the theorem is implicitly present in all scientific models and engineering computations involving spatial relationships or trigonometry. An invisible companion to the dot-product operation, it is inherent in equations of mathematical ph...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Selecciones Matemáticas
سال: 2017
ISSN: 2411-1783
DOI: 10.17268/sel.mat.2017.01.01