The field of constructible lengths, part 2

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, \mathbb K, 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 x-axis.

The second idea is going to be looking \mathbb K by starting with \mathbb Q and building it up piece-by-piece.

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