Without Equations, Conics & Spirals 
Without Equations, Conics & Spirals
by Richard Southwell
Video Lecture 2 of 16
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Date Added: March 5, 2015

Lecture 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.

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/

Course Index

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.

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