An application of Grossone to the study of a family of tilings of the hyperbolic plane

TL;DR

This paper explores how Sergeyev's grossone numeral system enhances the analysis of hyperbolic plane tilings, providing new insights and greater precision compared to traditional methods.

Contribution

It introduces the application of grossone to hyperbolic tilings, revealing different perspectives and improving the accuracy of existing results.

Findings

Different analysis perspectives depend on the viewing approach.

The grossone system confirms some traditional results.

It offers additional precision in understanding hyperbolic tilings.

Abstract

In this paper, we look at the improvement of our knowledge on a family of tilings of the hyperbolic plane which is brought in by the use of Sergeyev's numeral system based on grossone. It appears that the information we can get by using this new numeral system depends on the way we look at the tilings. The ways are significantly different but they confirm some results which were obtained in the traditional but constructive frame and allow us to obtain an additional precision with respect to this information.