Multidimensional integer trigonometry
type: Item
instance of: scholarly article
title: Multidimensional integer trigonometry
author: John Blackman
author: James G. Dolan
author: Oleg Karpenkov
published in: Communications in Mathematics
publication date: 2024-08-28T00:00:00Z
review text: In this paper, the authors generalize integer trigonometric functions from two dimensions into arbitrary dimensions. They give a definition of the integer sine of a simplicial cone relating it to integer volume and give a definition of integer arctangent and relate it to Hermite's normal form. This leads naturally to describing the relationship between the values of adjacent cones, transpose cones, and cones which generate the same simplex. This leads to a notion of best approximations of simplicial cones. They also discuss the relationship between integer trigonometry, the Euclidean Algorithm, and continued fractions.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 52B20
zbMATH DE Number: 7902969
zbMATH Keywords: lattice geometry
zbMATH Keywords: multidimensional Euclidean algorithms
zbMATH Keywords: best approximations
MaRDI profile type: Publication
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DOI: 10.46298/CM.10919
description: scientific article; zbMATH DE number 7902969