Computing the distance between points on a plane is a trivial matter once we erect a Cartesian coordinate system on it—we simply use equation (7.1). Seen from a three—dimensional vantage point, the plane may have any position or orientation we like. If we choose to remain “in” the plane, we can regard it as a two—dimensional space in its own right: the possibility of erecting Cartesian coordinates upon it, and using equation (7.1) to measure distances between its points, characterizes it as a “flat” or Euclidean space.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Non—Euclidean Geometry. In: Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Geometry and Computing, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73398-0_10
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DOI: https://doi.org/10.1007/978-3-540-73398-0_10
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