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Imaginary elements in geometry

Name: Imaginary elements in geometry
Availability: InStock
ISBN: 9783723517475

Von de Boer, L.A.D.

Herausgegeben von Verlag am Goetheanum

English 180 Seiten 2024 ISBN 9783723517475

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Über dieses Buch

A remarkable fact in mathematics is the accordance between algebra and geometry: since the time of Descartes it is possible to express geometric phenomena in terms of numbers. And after doing calculations with these numbers, we can draw geometric conclusions from them. However, soon it appeared that, for instance, a circle and a line outside that circle have 'imaginary' meeting points: points that have imaginary coordinates but can not be found in the figure. Karl von Staudt found a brilliant way to visualize imaginary geometric points, lines and planes, and Felix Klein simplified and extended his method. In this book imaginary elements appear as Klein-movements in our real space. Apart from its mathematical importance, these movements may be seen as an alternative for the remarkable occurrences of complex numbers in physics, viz. quantum physics.