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Is the mentioned proof about not being able to create a transcendental number length segment with a compass and straight edge, I think I'm missing the boundarie
by Glyptodon 5y ago
Is the mentioned proof about not being able to create a transcendental number length segment with a compass and straight edge, I think I'm missing the boundaries of how constructions are permitted within the proof. Is this effectively because you need more than 2 linkages to translate curved motion to linear motion? (As I'd assume any device that converts circular motion to linear motion would produce linear motion in ratios of pi.)
- Jtsummers 5y agohttps://en.wikipedia.org/wiki/Constructible_number https://en.wikipedia.org/wiki/Constructible_number That is the definition of "constructible". In order to perform (with straightedge and compass) the squaring of the circle, you need to construct a line of length sqrt(pi) in a finite number of steps. However, since sqrt(pi) is a transcendental number, that's impossible.