Hi, I'm Katie. I'm a freshman from Hastings, Nebraska, and probably a math major. I've decided to do my project on the compass and straightedge. There are a lot of interesting stories involving the Greeks and their attempts at squaring a circle, trisecting an angle, doubling a cube, constructing something with length pi, and so on. The compass and straightedge represent very abstract ideas, and rarely serve a practical purpose. A theoretical compass is supposed to be automatically collapsible, for example, but a physical compass can record lengths. A straightedge is only supposed to have one dimension. Otherwise it could construct certain angles or compare lengths. Basically, the compass and straightedge do less work than they can.
From regentsprep.org/Regents/math/construc/construct.htm
The problems of antiquity took centuries to prove impossible and problems of constructible numbers and figures are still around. Meanwhile, middle school students still play with compasses and rulers when learning basic geometry. I'd like to go into the history of the instruments and how they are used today, as well as how these instruments changed mathematical thought.
I'd love to hear any ideas you all have!
Feel free to send me comments or questions here---> klhoward@stanford.edu
Here is my project---> Compass and Straightedge
Posted at Feb 13/2006 12:28AM:
Michael Shanks: scientific instruments make great subjects - if you do opt for this remind me to put you on to the likes of Bruno Latour and science studies and their view of instrumentation
Posted at Feb 21/2006 11:41AM:
[klfsong]: You might want to look into the aesthetic appeal. Now they can by pink and sparkly. Why do they need to be? What does that say about our culture?
Posted at Feb 26/2006 04:32PM:
Daniel Steinbock: This is a great topic. Not many are aware that geometry was born out of these two abstract -- non-physical, analytic -- tools. A geometrical figure was not considered valid unless it could be constructed using only (collapsing) compass and (one-dimensional) straightedge. The contrast between the abstract and the physical tools is very interesting. On one hand, the construction rule is meant to ground geometry is physical reality; on the other, it still assumes impossible things liks one-dimensional objects. You could look closer at the separation of abstract mathematical universes from physicality. You might also connect this to other abstract, analytic tools used by mathematicians, scientists or engineers.
Posted at Mar 14/2006 12:22AM:
Chun Kai Wang: It is quite interesting how you can do many things with just a compass and a straight edge. Especially bisecting an angle. You can achieve it perfectly with a compass and straight edge- something imprecise even with a protractor.
