The field of constructible lengths, part 2
October 9, 2011 Leave a comment
Sorry for the delay. It turns out graduate school is time consuming. I think I will probably knock down my daily posting to 5 days a week. I suppose I’ll play it by ear.
This field of constructible lengths, , that we talked about last time is somewhat mysterious, and we want to illuminate it a bit more. What does it look like? There are two important ideas here. The first is that instead of thinking about constructible distances, I want to think about all the real numbers that can be coordinates of a point we can construct. A little thought tells us that these are the same fields. We can translate points to the origin, and then draw a circle to rotate one onto the -axis.
The second idea is going to be looking by starting with and building it up piece-by-piece.