Abstract
Tarski showed in the 1950s that (first-order) questions in Euclidean geometry could be answered algorithmically. Algorithms for doing this have greatly improved over the decades but still have high complexity (in terms of time taken). We experiment using state-of-the-art software, specifically so-called SMT Solvers, to see how practical it is to prove classical Euclidean geometry results in this way.
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Emil Artin, Geometric Algebra, Dover Books on Mathematics, Dover Publications Inc., 2016.
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Siddhartha Gadgil is a Professor of Mathematics at Indian Institute of Science, Bengaluru. He has a PhD in Mathematics from California Institute of Technology and a B.Stat degree from Indian Statistical Institute, Kolkata. He began his research career in (low dimensional) topology and worked for many years in that and related fields. In recent years, the primary focus of his research has been automated theorem proving.
Anand Rao Tadipatri is a fourth year BS-MS student at IISER Pune. He is interested in mathematics in general, and areas related to mathematical logic and foundations in particular. He has lately been experimenting with the Lean Theorem Prover and programming language.
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Gadgil, S., Tadipatri, A. Euclidean Geometry by High-performance Solvers?. Reson 27, 801–816 (2022). https://doi.org/10.1007/s12045-022-1373-7
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DOI: https://doi.org/10.1007/s12045-022-1373-7