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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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...
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PYTHAGOREAN THEOREM AND CORRESPONDING FUNCTIONAL EQUATIONS
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It is shown that the most important effects of special and general theory of relativity can be understood in a simple and straightforward way. The system of units in which the speed of light c is the unit of velocity allows to cast all formulas in a very simple form.The Pythagorean theorem graphically relates energy, momentum and mass. The paper is addressed to those who teach and popularize th...
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ژورنال
عنوان ژورنال: Science
سال: 1911
ISSN: 0036-8075,1095-9203
DOI: 10.1126/science.33.847.457