naa a22 4500 510737145 CHVBK 20180411083014.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s13366-012-0097-3 doi (NATIONALLICENCE)springer-10.1007/s13366-012-0097-3 Müller Christian Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedener Hauptstraße 8-10/104, 1040, Vienna, Austria aut Discretizations of the hyperbolic cosine [Elektronische Daten] [Christian Müller] This paper explores different notions of a discrete hyperbolic cosine. The interest in this topic arises from the discretization of the catenoid which is a minimal surface of revolution and whose meridian curve is the hyperbolic cosine. Different but equivalent characterizations of the smooth hyperbolic cosine function lead to different discretizations which are no longer equivalent. However, it turns out that there are still some interrelations. We are led to some explicit and recursive definitions. It is also natural that we study discretizations of the tractrix whose evolute is the hyperbolic cosine, and its relation to discrete surfaces of constant Gaussian curvature. We can show convergence results for the discrete hyperbolic cosine and the discrete tractrix to their smooth counterparts. The Managing Editors, 2012 Discrete differential geometry nationallicence Discrete catenoid nationallicence Discrete hyperbolic cosine nationallicence Discrete tractrix nationallicence Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Berlin Heidelberg 54/2(2013-10-01), 509-531 0138-4821 54:2<509 2013 54 13366 https://doi.org/10.1007/s13366-012-0097-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-012-0097-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Müller Christian Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedener Hauptstraße 8-10/104, 1040, Vienna, Austria aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Berlin Heidelberg 54/2(2013-10-01), 509-531 0138-4821 54:2<509 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer