The Line Woven Net 
The Line Woven Net
by Richard Southwell
Video Lecture 9 of 16
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Date Added: March 5, 2015

Lecture Description

The woven net (also known as the complete harmonic quadrangle-quadrilateral net) is a beautiful construction which begins with a quadrilateral (four points), and grows inwardly and outwardly as one repeatedly creates quadrilaterals (four lines) from quadrangles, which are dual to each other. Although many deep ideas can be seen by meditating on this construction, ultimately one just needs a pencil and a straight edge to make one. Essentially the woven net is a way to fill the projective plane by repeatedly creating `Thirteen Configurations'.

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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