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Shape-regular polygons in finite planes

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Abstract

The notion of shape in the Gaussian plane was introduced by Lester [5] and extended by Artzy [1]. In this paper we generalize this notion in the affine planesAG(2,q) over the Galois fieldGF(q), q=p r andp an odd prime. We investigate the existence of shape-regular polygons and the correspondence between shape-regularity and affine-regularity.

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References

  1. Artzy, R.:Shapes of polygons, J. Geometry 50 (1994), 11–15.

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  4. Korchmáros, G.:Poligoni affin-regolari dei piani di Galois d'ordine dispari, Rend. dell'Acc. Naz. Lincei 56 (5) 1974, 690–697.

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  5. Lester,J.A.:Triangles I: Shapes. Forthcoming, Aequationes Math.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Rafael Artzy

  2. Department of Geometry, Eötvös Loránd University, Rákóczi u. 5, H-1088, Budapest, Hungary

    György Kiss

Authors
  1. Rafael Artzy
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  2. György Kiss
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Dedicated to the memory of Giuseppe Tallini

The work was supported by the Hungarian National Foundation for Scientific Research, Grant No. F016302 and T017314.

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Artzy, R., Kiss, G. Shape-regular polygons in finite planes. J Geom 57, 20–26 (1996). https://doi.org/10.1007/BF01229247

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  • DOI: https://doi.org/10.1007/BF01229247

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