
Lecture Description
We continue our study of projective transformations of the line, and study what configurations cause involutions. An involution is
a transformation which leaves positions unaltered, when applied twice. Interestingly, our questions about involutions quickly
return us to the consideration of harmonic quadrilaterals.
Course Index
- Why Perspective Drawing Works
- Without Equations, Conics & Spirals
- Foundations & Tilings in Perspective
- When Does A Parabola Look Like An Ellipse?
- Desargues' Theorem Proof
- Axioms, Duality and Projections
- Conics Made Easily and Beautifully
- Harmonic Quadrangles & The 13 Configuration
- The Line Woven Net
- Brianchon's Theorem (Pascal's Dual)
- Five Points Define A Conic
- Projective Transformations Of Lines
- Involutions Of The Line
- Constructing The Dual Of A Quadrangle - The Thirteen Point Configuration
- Pascal's Hexagrammum Mysticum Theorem
- Non Euclidean Geometry & Hyperbolic Social Networks
Course Description
Protective geometry is deeper and more fundamental than standard euclidean geometry, and has many applications in fundamental physics, biology and perspective drawing. We shall introduce it visually, without relying upon equations. The hope is make this beautiful subject accessible to anybody, without requiring prior knowledge of mathematics. At the same time, there are some very deep, rarely discussed ideas in this subject which could also benefit experts.