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 languageEnglish
Title of host publicationProceedings of Bridges Baltimore 2015 : Mathematics, Music, Art, Architecture, Culture
Publication date2015
Pages379-382
Publication statusPublished - 2015
EventBridges Baltimore 2015 - The University of Baltimore, Baltimore, Maryland, United States
Duration: 29 Jul 20151 Aug 2015
http://bridgesmathart.org/

Conference

ConferenceBridges Baltimore 2015
LocationThe University of Baltimore
CountryUnited States
CityBaltimore, Maryland
Period29/07/201501/08/2015
Internet address

Cite this

Brander, D., & Markvorsen, S. (2015). Surfaces with Natural Ridges. In Proceedings of Bridges Baltimore 2015: Mathematics, Music, Art, Architecture, Culture (pp. 379-382)
Brander, David ; Markvorsen, Steen. / Surfaces with Natural Ridges. Proceedings of Bridges Baltimore 2015: Mathematics, Music, Art, Architecture, Culture. 2015. pp. 379-382
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Brander, D & Markvorsen, S 2015, Surfaces with Natural Ridges. in Proceedings of Bridges Baltimore 2015: Mathematics, Music, Art, Architecture, Culture. pp. 379-382, Bridges Baltimore 2015, Baltimore, Maryland, United States, 29/07/2015.

Surfaces with Natural Ridges. / Brander, David; Markvorsen, Steen.

Proceedings of Bridges Baltimore 2015: Mathematics, Music, Art, Architecture, Culture. 2015. p. 379-382.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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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.

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Brander D, Markvorsen S. Surfaces with Natural Ridges. In Proceedings of Bridges Baltimore 2015: Mathematics, Music, Art, Architecture, Culture. 2015. p. 379-382