Free Segments of a Neutral Plane (FSEG)

Edward John Specht, Harold Trainer Jones, Keith G. Calkins and Donald H. Rhoads
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Edward John Specht: Indiana University South Bend
Harold Trainer Jones: Andrews University
Keith G. Calkins: Ferris State University
Donald H. Rhoads: Andrews University

Chapter Chapter 9 in Euclidean Geometry and its Subgeometries, 2015, pp 225-233 from Springer

Abstract: 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.

Date: 2015
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DOI: 10.1007/978-3-319-23775-6_9

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