Abstract
Free segments are defined as congruence classes of segments; these are ordered in a natural way, and this ordering is shown to be transitive and to have the trichotomy property. Addition of free segments is defined, and its elementary properties and interactions with ordering are studied. These developments are sufficient to prove the triangle inequality, and provide a first step toward defining distance on a neutral plane.
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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). Free Segments of a Neutral Plane (FSEG). In: Euclidean Geometry and its Subgeometries. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-23775-6_9
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DOI: https://doi.org/10.1007/978-3-319-23775-6_9
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-23774-9
Online ISBN: 978-3-319-23775-6
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