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Reflections in Hyperbolic Geometry - Universal Hyperbolic Geometry Lecture 14

Insights into Mathematics via YouTube

Overview

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This lecture introduces reflections in universal hyperbolic geometry, comparing them with Euclidean reflections and showing how point reflections relate to reflections in dual lines.

Syllabus

Introduction, symmetries of a geometry, types of symmetries
Reflections in Euclidean geometry: 1 dimension
Reflections in Euclidean geometry: 2 dimensions
Reflections in Universal Hyperbolic Geometry
Reflections in a point
Reflections also act on lines
example of reflections in point_a outside and its dual
example of reflections in point_a inside the circle

Taught by

Insights into Mathematics

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