Geometry of Convex Closed Plane Curves
碩士 === 國立清華大學 === 數學系 === 102 === In the first five sections we introduce some important geometric quantities of a curve, such as curvature, torsion, the support function and the width. In the rest part of this thesis we derive some famous geometric inequalities such as the isoperimetric inequality,...
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| Format: | Others |
| Language: | en_US |
| Published: |
2014
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| Online Access: | http://ndltd.ncl.edu.tw/handle/skmzds |
| Summary: | 碩士 === 國立清華大學 === 數學系 === 102 === In the first five sections we introduce some important geometric quantities of a curve, such as curvature, torsion, the support function and the width. In the rest part of this thesis we derive some famous geometric inequalities such as the isoperimetric inequality, Gage’s isoperimetric inequality and Wirtinger inequality. Also we introduce an important idea for a curve – the parallel curve. Using the idea of the parallel curve we can obtain our final goal of this thesis – the entropy estimate.
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