Formalizing complex plane geometry

4 years 10 months ago
Formalizing complex plane geometry
Deep connections between complex numbers and geometry had been well known and carefully studied centuries ago. Fundamental objects that are investigated are the complex plane (usually extended by a single infinite point), its objects (points, lines and circles), and groups of transformations that act on them (e.g., inversions and M¨obius transformations). In this paper, we treat the geometry of complex numbers formally and present a fully mechanically verified development within the theorem prover Isabelle/HOL. Apart from applications in formalizing mathematics and in education, this work serves as a ground for formally investigating various non-Euclidean geometries and their intimate connections. We discuss different approaches to formalization and discuss the major advantages of the more algebraically oriented approach. Keywords Interactive theorem proving · Complex plane geometry · M¨obius transformations
Filip Maric, Danijela Petrovic
Added 15 Apr 2016
Updated 15 Apr 2016
Type Journal
Year 2015
Where AMAI
Authors Filip Maric, Danijela Petrovic
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