We describe a remarkable implication of Pascal's theorem,
which is that given any 5 points in the plane (no 3 of which are co-linear), there
exists a single conic curve which passes through the 5 points. It also follows, by duality, that
a conic is uniquely defined by specifying 5 lines which are tangent to it.

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.