Continued fractions and the second Kepler law

TL;DR

This paper explores the connection between the geometry of continued fractions and Keplerian trajectories, extending geometric interpretations to more general continued fractions with arbitrary elements.

Contribution

It introduces a novel link between continued fractions and Kepler's second law, broadening the geometric understanding of continued fractions beyond traditional cases.

Findings

Established a geometric interpretation of continued fractions related to Keplerian motion

Extended the geometric interpretation to continued fractions with arbitrary elements

Provided insights into the structure of trajectories in relation to continued fractions

Abstract

In this paper we introduce a link between geometry of ordinary continued fractions and trajectories of points that moves according to the second Kepler law. We expand geometric interpretation of ordinary continued fractions to the case of continued fractions with arbitrary elements.