One dimensional metrical geometry

Details One dimensional metrical geometry One dimensional metrical geometry

2007-01-12

arxiv.org/abs/math/0701338v1

Mathematics

Metric Geometry

19 pages

Scientific paper

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.

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