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Why All Maps Are Wrong - Theorema Egregium

Mathemaniac via YouTube

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Overview

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This course presents a geometric proof of the Theorema Egregium and explains why no world map can preserve both areas and angles. It covers curvature, spherical areas, geodesics, parallel transport, and holonomy.

Syllabus

Introduction
Chapter 1: Curvature
Chapter 2: Spherical areas
Chapter 3.1: Gauss map preserves parallel transport
Chapter 3.2: Geodesics preserved
Chapter 3.3: Parallel transport preserved
Chapter 3.4: Area = holonomy on sphere
Chapter 4: Tying everything together

Taught by

Mathemaniac

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