Maria Teresa Calapso’s Hyperbolic Pythagorean Theorem
نویسندگان
چکیده
منابع مشابه
The 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."
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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...
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new form of the Hyperbolic Pythagorean Theorem, which has a striking t e intuitive appeal and offers a strong contrast to its standard form, is presented. I xpresses the square of the hyperbolic length of the hypotenuse of a hyperbolic s o right angled triangle as the "Einstein sum" of the squares of the hyperbolic length f the other two sides, Fig. 1, thus completing the long path from Pythago...
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ژورنال
عنوان ژورنال: The Mathematical Intelligencer
سال: 2010
ISSN: 0343-6993,1866-7414
DOI: 10.1007/s00283-010-9169-0