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Formalization of the Poincaré disc model of hyperbolic geometry. (English) Zbl 07356967

Summary: We describe formalization of the Poincaré disc model of hyperbolic geometry within the Isabelle/HOL proof assistant. The model is defined within the complex projective line \(\mathbb{C}{}P^1\) and is shown to satisfy Tarski’s axioms except for Euclid’s axiom – it is shown to satisfy it’s negation, and, moreover, to satisfy the existence of limiting parallels axiom.

MSC:

68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)
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