Elementary notions of lattice trigonometry

Karpenkov, Oleg ORCID: 0000-0002-3358-6998 (2006) Elementary notions of lattice trigonometry The first part in Math. Scand., 2 (2). pp. 221-239. ISSN 0025-5521

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Abstract

In this paper we study properties of lattice trigonometric functions of lattice angles in lattice geometry. We introduce the definition of sums of lattice angles and establish a necessary and sufficient condition for three angles to be the angles of some lattice triangle in terms of lattice tangents. This condition is a version of the Euclidean condition: three angles are the angles of some triangle iff their sum equals π. Further we find the necessary and sufficient condition for an ordered n-tuple of angles to be the angles of some convex lattice polygon. In conclusion we show applications to theory of complex projective toric varieties, and a list of unsolved problems and questions.

Item Type:	Article
Additional Information:	49 pages; 16 figures
Uncontrolled Keywords:	math.CO, math.CO, math.NT
Depositing User:	Symplectic Admin
Date Deposited:	09 May 2016 10:05
Last Modified:	21 Apr 2026 20:13
Related Websites:	Author
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3001123
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