Doron -
first of all I'd like to point out that your document is beautifully executed!
But I'm not quite sure I get the point of your question. I am not a mathematician but I'd like to understand what you are asking about.
As far as I know, the Archimedean Spiral is based on Phi, also known as the "golden ratio". So it's no wonder you get all these beautiful spirals and shapes.
Do you mind explaining what you mean by question 4?
For interested folks - here is a site about Phi:
http://www.mcs.surrey.ac.uk/Personal...nacci/phi.html
Tormod