Elementary notions of lattice trigonometry

Karpenkov, Oleg ORCID: 0000-0002-3358-6998
(2006) Elementary notions of lattice trigonometry. 2008. The second part in Funct. Anal. Other Math., 2 (2). pp. 2-4.

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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 \pi. 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, 11H06, 52B20
Depositing User: Symplectic Admin
Date Deposited: 09 May 2016 10:05
Last Modified: 19 Jan 2023 07:37
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3001123