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Geometriae Dedicata

, Volume 128, Issue 1, pp 145–166 | Cite as

One dimensional metrical geometry

  • N. J. Wildberger
Original Paper

Abstract

One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this situation, such as the Triple quad formula, the Triple spread formula and the Spread polynomials, which are universal analogs of the Chebyshev polynomials of the first kind. Chromogeometry appears here, and the related metrical and algebraic properties of the projective line are brought to the fore.

Keywords

Metrical geometry Rational trigonometry One dimensional Quadrance Spread Chromogeometry Universal geometry 

Mathematics Subject Classification (2000)

51F99 51N25 14A99 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUNSWSydneyAustralia

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