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New Families Of Embedded Triply Periodic Minimal Surfaces Of Genus Three In Euclidean Space, Adam G. Weyhaupt
New Families Of Embedded Triply Periodic Minimal Surfaces Of Genus Three In Euclidean Space, Adam G. Weyhaupt
All Theses, Dissertations, and Capstone Projects
Until 1970, all known examples of embedded triply periodic minimal surfaces (ETPMS) contained either straight lines or curves of planar symmetry. In 1970, Alan Schoen discovered the gyroid, an ETPMS that contains neither straight lines nor planar symmetry curves. Meeks discovered in 1975 a 5-parameter family of genus 3 ETPMS that contained all known examples of genus 3 ETPMS except the gyroid. A second example lying outside the Meeks family was proposed by Lidin in 1990. Große-Brauckmann and Wohlgemuth showed in 1996 the existence and embeddedness of the gyroid and “Lidinoid”. In a series of investigations the scientists, Lidin, et. …
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Theses Digitization Project
The goal of the thesis is to study geodesics on surfaces of constant Gaussian curvature. The first three sections of the thesis is dedicated to the definitions and theorems necessary to study surfaces of constant Gaussian curvature. The fourth section contains examples of geodesics on these types of surfaces and discusses their properties. The thesis incorporates the use of Maple, a mathematics software package, in some of its calculations and graphs. The thesis' conclusion is that the Gaussian curvature is a surface invariant and the geodesics of these surfaces will be the so-called best paths.