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.

[img] Text
0604129v3.pdf - Unspecified

Download (461kB)

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 \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