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.

To get into this visual mindset we discus conics. We describe ellipses, hyperbola and parabola, and how they appear in astronomy, optics, and projectile movement. We show how these curves can be thought can thought of as conic sections, and how the Geogebra program called can be used to study these ideas.

We also discuss how logarithmic spirals occur in sunflowers, weather systems, and galaxy spirals, and we describe a simple geometric method for constructing them.

The subject matter in this introductory video is not exclusive to projective geometry. It was chosen to start the visual approach.

The Geogebra program can be found here:
www.geogebra.org/

I would like to thank Olive Whicher for his illuminating book on projective geometry, and Norman Wildberger for his insightful teachings on the subject.

I also cited a result from

Hilton, P.; Holton, D.; and Pedersen, J. Mathematical Reflections in a Room with Many Mirrors. New York: Springer-Verlag, 1997.

I also use the following Wolfram Demonstration (by Phil Ramsden):

demonstrations.wolfram.com/ConicSectionsTheDoubleCone/

My website is:

sites.google.com/site/richardsouthwell254/

1. Why Perspective Drawing Works
2. Without Equations, Conics & Spirals
3. Foundations & Tilings in Perspective
4. When Does A Parabola Look Like An Ellipse?
5. Desargues' Theorem Proof
6. Axioms, Duality and Projections
7. Conics Made Easily and Beautifully
8. Harmonic Quadrangles & The 13 Configuration
9. The Line Woven Net
10. Brianchon's Theorem (Pascal's Dual)
11. Five Points Define A Conic
12. Projective Transformations Of Lines
13. Involutions Of The Line
14. Constructing The Dual Of A Quadrangle - The Thirteen Point Configuration
15. Pascal's Hexagrammum Mysticum Theorem
16. Non Euclidean Geometry & Hyperbolic Social Networks

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.