We, on the surface, at least, seem to have a tempermental difference. I guess I need to feel that I have outgrown the old paradigms before I go searching for new ones with too much vigor. Don't give myself that much credit.
Yes. Point taken. I bit my tongue even as I typed those hazylazy words "new paradigm". Let me re-phrase.. This looks like a good idea, and I hope is progress.
Geometry is about as old a paradigm as there gets. It seems to have kept me busy enough for a good stretch now. I espouse a paradigm of sitting down with compass and ruler and doing Euclid - soup to nuts. As a start.
I love a good compass - especially the older ones, with nibs for ink.
mmm yes. Let's go Egyptian string sand and sea shells :-) For years I treasured a little second hand Russian pamphlet I found on the Charing Cross road. 'Geometry with [only] rulers and compass' - meaning straighedge no measurements or protractors. A similar epiphany, but a lot more complex+expensive, was seeing Tom Davis's 'Geometer' running on an SGI for the first time about 10 years ago. http://www.sgi.com/fun/freeware/software.html [A cousin/ancestor of Geometer's Sketchpad] He's now involved in Math circles: http://www.geometer.org/mathcircles/index.html ...which perhaps proves that this stuff really goes to your head! ./Jason