Isometry Groups of the Projective Line - Rational Geometry Math Foundations

Explore the algebraic approach to the metrical structure of the projective line in this 35-minute video lecture. Discover how isometry groups, including rotations and reflections, can be defined and studied over finite fields. Examine the projective line using fields F3 and F5, uncovering significant differences between these cases and revealing aspects of Euclidean geometry not visible in rational number settings. Learn how this finite Euclidean geometry connects with relativistic geometry and serves as an introduction to relativistic thinking. Delve into topics such as notation for projective points, group multiplication tables, and formulas for projective rotations and reflections. Gain insights into this remarkable meeting ground of traditional geometry and combinatorial domains, opening new avenues for investigation and enumeration in finite settings.

Intro to projective metrical structure
Notation for projective points
Exercise
The projective line
Rotations and reflections
A group multiplication table
The projective line p_1 over F5
Formulas for projective rotations and reflections