Flat Circle Planes as Integrals of Flat Affine Planes

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In a previous article (Arch. Math. 64 (1995), 75-85) we showed that flat Laguerre planes can be constructed by 'integrating' flat affine planes. It turns out that 'most' of the known flat Laguerre planes arise in this manner. In this paper we show that similar constructions are also possible in the case of the other two kinds of flat circle planes, that is, the flat Möbius planes and the flat Minkowski planes. In particular, we show that many of the known flat Möbius planes can be constructed by integrating a closed strip taken from a flat affine plane. We also show how flat Minkowski planes arise as integrals of two flat affine planes. All known flat Minkowski planes can be constructed in this manner.

Original languageEnglish
Pages (from-to)149-162
Number of pages14
JournalGeometriae Dedicata
Issue number2
Publication statusPublished - 1997
Externally publishedYes


  • Affine plane
  • Circle plane
  • Integration

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