Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Gold Open Access
Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Volume formulae for regular hyperbolic cubes


Author: T. H. Marshall
Journal: Conform. Geom. Dyn. 2 (1998), 25-28
MSC (1991): Primary 51M10, 51M25, 52A35, 52A38; Secondary 05B45, 51M20, 52A40
Published electronically: February 11, 1998
MathSciNet review: 1600384
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We express the volume of a regular cube in hyperbolic $n$-space as an integral on $[0, \infty)$, and derive from this an asymptotic volume formula for the regular ideal hyperbolic $n$-cube. This in turn is applied to finding an asymptotic lower bound for the least number of simplices into which a Euclidean $n$-cube can be triangulated.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (1991): 51M10, 51M25, 52A35, 52A38, 05B45, 51M20, 52A40

Retrieve articles in all journals with MSC (1991): 51M10, 51M25, 52A35, 52A38, 05B45, 51M20, 52A40


Additional Information

T. H. Marshall
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Email: t_marshall@math.auckland.ac.nz

DOI: http://dx.doi.org/10.1090/S1088-4173-98-00025-3
PII: S 1088-4173(98)00025-3
Keywords: Hyperbolic cube, volume, simplex, triangulation
Received by editor(s): August 15, 1997
Received by editor(s) in revised form: November 26, 1997
Published electronically: February 11, 1998
Article copyright: © Copyright 1998 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia