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Galileo UnboundA Path Across Life, the Universe and Everything$
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David D. Nolte

Print publication date: 2018

Print ISBN-13: 9780198805847

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198805847.001.0001

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Geometry on my Mind

Geometry on my Mind

Chapter:
(p.95) Chapter 5 Geometry on my Mind
Source:
Galileo Unbound
Author(s):

David D. Nolte

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198805847.003.0005

This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics. Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics. Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems in chaos theory. Motion cannot exist without space—trajectories are the tracks of points, mathematical or physical, through it.

Keywords:   history of mathematics, Gauss, Riemann, manifold, non-Euclidean geometry, curvature, Göttingen, Felix Klein, Grassmann, Peano, Hausdorff, fractal

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