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YouTube

The Discrete Charm of Geometry by Alexander Bobenko

International Centre for Theoretical Sciences via YouTube

Overview

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This course aims to introduce learners to the foundations of a new branch of mathematics focusing on discrete geometric structures. The learning outcomes include understanding the paradigm of structure-preserving discretizations through various real-world examples such as toy spinning tops, elastic rods, and conformal texture mappings in computer graphics. The course teaches skills in geometric integration, practical applications of discrete geometry in modeling and approximating continuous shapes, and constructing mathematical surfaces. The teaching method involves a non-technical and pictorial approach, with the intended audience being individuals interested in mathematics, geometry, computer graphics, and real-world applications of discrete geometric structures.

Syllabus

Introduction
Discretization
Art
Geometric Integration
Metric Integration
Practical Applications
Elastic Rods
Elastic Curves
Discrete Analogs
Discrete Tangent Flow
Discrete Smokering Flow
Discrete Differential Geometry
Structure
Constructions
Mathematical surfaces
Curved glass
Flat maps
World map
Map projection
Stereographic projection
Mercatos map
Conformal maps
Informal maps

Taught by

International Centre for Theoretical Sciences

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