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The Circle and Projective Homogeneous Coordinates in Universal Hyperbolic Geometry - Lecture 7b

Offered By: Insights into Mathematics via YouTube

Tags

Projective Geometry Courses Conic Sections Courses Renaissance Art Courses Special Relativity Courses Perspective Drawing Courses Mathematical Physics Courses Parabolas Courses Universal Hyperbolic Geometry Courses

Course Description

Overview

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Learn about projective geometry and its connection to universal hyperbolic geometry in this 24-minute video lecture. Explore the 19th century view of projective space as one-dimensional subspaces of a higher-dimensional affine space. Discover how the projective line relates to lines through the origin in two-dimensional space, and how the projective plane deals with subspaces in three-dimensional xyz space. Examine the relationship between projective geometry and Renaissance artists' attempts at correct perspective rendering, illustrated through a novel look at parabolas. Understand the two-dimensional representation of the projective plane and its intersection with the z=1 plane in xyz space. Gain insights into how the circle represents a cone in this view, connecting back to ancient Greek geometry. Delve into the importance of the circle in projective homogeneous coordinates, a crucial concept in mathematics and physics, particularly in special relativity and hyperbolic geometry.

Syllabus

The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b


Taught by

Insights into Mathematics

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