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Morley’s triangles of a triangle in the isotropic plane

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Abstract

In this paper we define and study Morley’s triangles of a triangle in the isotropic plane. We derive the equations of angle trisectors of angles of the standard triangle in the isotropic plane, and utilizing them we get the coordinates of vertices of Morley’s triangles of the standard triangle. We investigate relationships between Morley’s triangles and the initial triangle, as well as connections with some other triangle elements in the isotropic plane. Finally, we consider some dual concepts of the introduced concepts.

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Acknowledgements

The authors would like to thank the referee for valuable comments which helped to improve the manuscript.

Funding

This research received no external funding.

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Authors and Affiliations

  1. Department of Natural Sciences, Faculty of Education, J. J. Strossmayer University of Osijek, Cara Hadrijana 10, 31000, Osijek, Croatia

    Ružica Kolar-Šuper

  2. Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Vladimir Volenec

Authors
  1. Ružica Kolar-Šuper
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  2. Vladimir Volenec
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Contributions

RKŠ and VV wrote the main manuscript text. RKŠ and VV prepared figures. All authors reviewed the manuscript.

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Correspondence to Ružica Kolar-Šuper.

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Kolar-Šuper, R., Volenec, V. Morley’s triangles of a triangle in the isotropic plane. J. Geom. 115, 21 (2024). https://doi.org/10.1007/s00022-024-00721-w

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  • DOI: https://doi.org/10.1007/s00022-024-00721-w

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