A Free Group of Rotations of Rank 2

Jagadish Bapanapally
(University of Wyoming)
Ruben Gamboa
(University of Wyoming)

One of the key steps in the proof of the Banach-Tarski Theorem is the introduction of a free group of rotations. First, a free group of reduced words is generated where each element of the set is represented as an ACL2 list. Then we demonstrate that there is a one-to-one relation between the set of reduced words and a set of 3D rotations. In this paper we present a way to generate this set of reduced words and we prove group properties for this set. Then, we show a way to generate a set of 3D matrices using the set of reduced words. Finally we show a formalization of 3D rotations and prove that every element of the 3D matrices set is a rotation.

In Rob Sumners and Cuong Chau: Proceedings Seventeenth International Workshop on the ACL2 Theorem Prover and its Applications (ACL2 2022), Austin, Texas, USA, 26th-27th May 2022, Electronic Proceedings in Theoretical Computer Science 359, pp. 76–82.
Published: 24th May 2022.

ArXived at: http://dx.doi.org/10.4204/EPTCS.359.8 bibtex PDF
References in reconstructed bibtex, XML and HTML format (approximated).
Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org