Abstract
This chapter is concerned with an arbitrary line in a Euclidean plane. It uses translations to define an operation of addition, and dilations to define multiplication on such a line; when equipped with these operations, the line becomes a field (defined in Chapter 1 Section 1.5). An ordering of the line is defined, so that the line becomes an ordered field. These concepts are used to define distance between points, and the length of a segment.
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References
Ewald, G.: Geometry: An Introduction. Ishi Press (2013). ISBN 978-4871877183
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© 2015 Springer International Publishing Switzerland
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Specht, E.J., Jones, H.T., Calkins, K.G., Rhoads, D.H. (2015). Every Line in a Euclidean Plane Is an Ordered Field (OF). In: Euclidean Geometry and its Subgeometries. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-23775-6_14
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DOI: https://doi.org/10.1007/978-3-319-23775-6_14
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-23774-9
Online ISBN: 978-3-319-23775-6
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