Conway river and Arnold sail
K. Spalding, A.P. Veselov
TL;DR
This paper reveals a straightforward connection between the Conway river, associated with real indefinite binary quadratic forms, and the Arnold sail, related to pairs of lines, bridging two geometric concepts in number theory.
Contribution
It introduces a novel relation linking the Conway river and Arnold sail, enhancing understanding of geometric structures in number theory.
Findings
Established a simple relation between Conway river and Arnold sail.
Bridged two geometric constructions in number theory.
Provided new insights into the structure of binary quadratic forms.
Abstract
We establish a simple relation between two geometric constructions in number theory: the Conway river of a real indefinite binary quadratic form and the Arnold sail of the corresponding pair of lines.
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Taxonomy
TopicsHistory and Theory of Mathematics · Mathematics and Applications · Analytic Number Theory Research