Surfaces with Natural Ridges

David Brander; Steen Markvorsen

Surfaces with Natural Ridges

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Abstract

We discuss surfaces with singularities, both in mathematics and in the real world. For many types of mathematical surface, singularities are natural and can be regarded as part of the surface. The most emblematic example is that of surfaces of constant negative Gauss curvature, all of which necessarily have singularities. We describe a method for producing constant negative curvature surfaces with prescribed cusp lines. In particular, given a generic space curve, there is a unique surface of constant curvature K = -1 that contains this curve as a cuspidal edge. This is an effective means to easily generate many new and beautiful examples of surfaces with constant negative curvature.

Original language	English
Title of host publication	Proceedings of Bridges Baltimore 2015 : Mathematics, Music, Art, Architecture, Culture
Publication date	2015
Pages	379-382
Publication status	Published - 2015
Event	Bridges Baltimore 2015 - The University of Baltimore, Baltimore, Maryland, United States Duration: 29 Jul 2015 → 1 Aug 2015 http://bridgesmathart.org/

Conference

Conference	Bridges Baltimore 2015
Location	The University of Baltimore
Country/Territory	United States
City	Baltimore, Maryland
Period	29/07/2015 → 01/08/2015
Internet address	http://bridgesmathart.org/

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Bridges2015 DBSMv3Accepted author manuscript, 8.17 MB
Bridges2015 379Final published version, 8.19 MB

http://archive.bridgesmathart.org/2015/bridges2015-379.html

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title = "Surfaces with Natural Ridges",

abstract = "We discuss surfaces with singularities, both in mathematics and in the real world. For many types of mathematical surface, singularities are natural and can be regarded as part of the surface. The most emblematic example is that of surfaces of constant negative Gauss curvature, all of which necessarily have singularities. We describe a method for producing constant negative curvature surfaces with prescribed cusp lines. In particular, given a generic space curve, there is a unique surface of constant curvature K = -1 that contains this curve as a cuspidal edge. This is an effective means to easily generate many new and beautiful examples of surfaces with constant negative curvature.",

author = "David Brander and Steen Markvorsen",

year = "2015",

language = "English",

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T1 - Surfaces with Natural Ridges

AU - Brander, David

AU - Markvorsen, Steen

PY - 2015

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N2 - We discuss surfaces with singularities, both in mathematics and in the real world. For many types of mathematical surface, singularities are natural and can be regarded as part of the surface. The most emblematic example is that of surfaces of constant negative Gauss curvature, all of which necessarily have singularities. We describe a method for producing constant negative curvature surfaces with prescribed cusp lines. In particular, given a generic space curve, there is a unique surface of constant curvature K = -1 that contains this curve as a cuspidal edge. This is an effective means to easily generate many new and beautiful examples of surfaces with constant negative curvature.

AB - We discuss surfaces with singularities, both in mathematics and in the real world. For many types of mathematical surface, singularities are natural and can be regarded as part of the surface. The most emblematic example is that of surfaces of constant negative Gauss curvature, all of which necessarily have singularities. We describe a method for producing constant negative curvature surfaces with prescribed cusp lines. In particular, given a generic space curve, there is a unique surface of constant curvature K = -1 that contains this curve as a cuspidal edge. This is an effective means to easily generate many new and beautiful examples of surfaces with constant negative curvature.

M3 - Article in proceedings

SP - 379

EP - 382

BT - Proceedings of Bridges Baltimore 2015

T2 - Bridges Baltimore 2015

Y2 - 29 July 2015 through 1 August 2015

ER -

Surfaces with Natural Ridges

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