3rd Online International Conference on
Quantum Physics and Nuclear Technology
April 13-14, 2022 | Virtual Conference
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Page 13
THE GAUSS’S, THEOREMA EGREGIUM
Peter G. Gyarmati
Public Understanding of Science and Mathematics, Hungary
Abstract
To understand Gauss’s theory about the non-Euclidean geometry we have to reestablish some definitions of the coordinate system and introduce the so-called Gaussian coordinates. We show here that the two points distance as a postulate can establish a metric geometry. If we can show the validity of this postulate on any surface than it has his geometry, and not necessarily Euclidean. Gauss showed in The Theorema Egregium that a surface might have such attributes. The different geometries of the regular surfaces written here are Euclidean, spherical, and hyperbolic. This theorem presented in 1827. (Based on the lectures of K. Lanczos: Department of Physical Sciences and Applied Mathematics, North Carolina State University, Raleigh, 1968.) The importance of this lecture is to make clear and understandable how and why the physicians use non-Euclidean geometry.
Biography
Peter G. Gyarmati received his engineering (electrical) and later the mathematical degree in Hungary than doctorate (1971) at Manchester University in computer science. Worked for IBM and ICL at their research center for networking: Aloha net and later on TCP/IP protocol. Also, have patents (1980) with portable computers. For invitation at 1998 went to the Stanford University to lead the introduction of the STEM type education. His mentor Edward Teller call his attention to the interdisciplinary of mathematics and physics. After some years (2008-2012) at Cambridge University, GB retired to Hungary. He wrote 18 books, and more than 50 research papers. His idea to show the importance of the non-Euclidean geometry.