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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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Cartesian coordinates

Cartesian coordinates

Chapter:
(p.11) 1 Cartesian coordinates
Source:
Relativity in Modern Physics
Author(s):

Nathalie Deruelle

Jean-Philippe Uzan

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198786399.003.0001

This chapter introduces Euclidean geometry, which provides the mathematical framework in which the laws of Newtonian physics are formulated. It first discusses how the concepts of ‘space’ and ‘relative, apparent, and common’ place are represented by a mathematical ensemble of points—the ‘absolute’ space ε‎3. A Cartesian frame of absolute space is materialized in ‘relative, apparent, and common’ space by a reference frame. Specifically, this reference frame is a solid trihedral—that is, an ensemble of physical objects whose relative distances are invariable in time and for which an orientation of the axes has been chosen. This chapter postulates that if the labeling of the points of ε‎3 is changed, the distance between two points remains unchanged. It then goes on to explain further the various associated formulas associated with Cartesian coordinates.

Keywords:   Cartesian coordinates, Euclidean geometry, absolute space, space, rigid displacements, point particle, Cartesian vectors, vector fields

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