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The Discrete Theorema Egregium.
- Source :
-
American Mathematical Monthly . January 2024, Vol. 131 Issue 1, p30-47. 18p. - Publication Year :
- 2024
-
Abstract
- In 1827, Gauss proved that Gaussian curvature is actually an intrinsic quantity, meaning that it can be calculated just from measurements within the surface. Before, curvature of surfaces could only be computed extrinsically, meaning that an ambient space is needed. Gauss named this remarkable finding Theorema Egregium. In this paper, we discuss a discrete version of this theorem for polyhedral surfaces. We give an elementary proof that the common extrinsic and intrinsic definitions of discrete Gaussian curvature are equivalent. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CURVATURE
*POLYHEDRAL functions
Subjects
Details
- Language :
- English
- ISSN :
- 00029890
- Volume :
- 131
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- American Mathematical Monthly
- Publication Type :
- Academic Journal
- Accession number :
- 174389703
- Full Text :
- https://doi.org/10.1080/00029890.2023.2263299