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Automated triangle constructions in hyperbolic geometry

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Abstract

We describe a system for automated ruler and compass triangle constructions in hyperbolic geometry. We discuss key differences between constructions in Euclidean and hyperbolic setting, compile a list of primitive constructions and lemmas used for constructions in hyperbolic geometry, build an automated system for solving construction problems, and test it on a corpus of triangle-construction problems. We extend the list of primitive constructions for hyperbolic geometry by several constructions that cannot be done by ruler and compass, but can be done by using algebraic calculations and show that such extended system solves more problems. We also use a dynamic geometry library to build an online compendium containing construction descriptions, illustrations, and step-by-step animations.

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Acknowledgements

This research is supported by the Serbian Ministry of Education, Science and Technological Development through the University of Belgrade, Faculty of Mathematics, Grant No. 451-03-47/2023-01/s200104. The research of the second author was supported by the Science Fund of the Republic of Serbia, Grant No. 7744592, Integrability and Extremal Problems in Mechanics, Geometry and Combinatorics - MEGIC.

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  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Serbia

    Vesna Marinković, Tijana Šukilović & Filip Marić

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  1. Vesna Marinković
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  2. Tijana Šukilović
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  3. Filip Marić
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Correspondence to Vesna Marinković.

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Tijana Šukilović and Filip Marić are contributed equally to this work.

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Marinković, V., Šukilović, T. & Marić, F. Automated triangle constructions in hyperbolic geometry. Ann Math Artif Intell 91, 821–849 (2023). https://doi.org/10.1007/s10472-023-09850-5

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