descriptive geometry and Gaspard Monge

I had the occasion recently to look into Monge's theorem and stumbled into
his work on drawing 3-D objects in 2D. It is that sort of late 18th century
stuff that portends projective geometry and is well worth looking into, I
think. There are a lot of those techniques that are very relevant nowadays.

 

http://en.wikipedia.org/wiki/Descriptive_geometry

 

In dealing with circles, I also found out about the problem of Apollonius of
Perga (272-190 BC) who showed there were eight distinct circles tangent to
any three non intersecting ones.

 

http://en.wikipedia.org/wiki/Problem_of_Apollonius

 

The SVG drawing illustrating the eight circles at the Wikipedia page is
quite cleverly drawn (though the code could be greatly simplified!). The
questions of how to make Venn diagrams that make the intersections maximally
distinguishable to the [typical] human eye is a fascinating one that has
received very little research (unless it has been done in secret!).

 

I didn't learn this sort of geometry in school, so it's quite a bit of fun!

 

Cheers

David



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