Explore the concept of reflections in hyperbolic geometry in this 31-minute lecture from the Universal Hyperbolic Geometry series. Begin with an overview of symmetries in geometry, including translations, rotations, and dilations. Examine reflections in Euclidean geometry for both one and two dimensions before delving into the hyperbolic version. Discover the surprising connection between reflections in a point and reflections in a dual line in hyperbolic geometry. Study examples of reflections both inside and outside a circle, gaining insights into the unique properties of hyperbolic space. Enhance your understanding of geometric symmetries and their applications in different mathematical frameworks.
Reflections in Hyperbolic Geometry - Universal Hyperbolic Geometry Lecture 14
Insights into Mathematics via YouTube
Overview
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
Related Courses
-
Quadrance and Spread - Universal Hyperbolic Geometry
-
The Circle and Cartesian Coordinates in Universal Hyperbolic Geometry - Lecture 5
-
Triangle Geometry Old and New - An Introduction to Hyperbolic Triangle Geometry
-
Geometer's Sketchpad and Circles in Universal Hyperbolic Geometry - Lecture 25
-
The Spread Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry
-
The Cross Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger
