Annals of Mathematics and Artificial Intelligence

, Volume 74, Issue 3, pp 271–308

Formalizing complex plane geometry

Article

DOI: 10.1007/s10472-014-9436-4

Cite this article as:
Marić, F. & Petrović, D. Ann Math Artif Intell (2015) 74: 271. doi:10.1007/s10472-014-9436-4
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Abstract

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 Möbius 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 provingComplex plane geometryMöbius transformations

Mathematics Subject Classifications (2010)

68T1551B1097I80

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia