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okay math majors honest question when is the last time you picked up one of these you remember these right compasses these things do you use in high school geometry class to maybe draw a circle or maybe bisect an angle or you know maybe construct a perpendicular or a parallel line or something like that its it was really cool you do some stuff with this and maybe 10th or 11th grade or whatever and then they sort of go away for a while but Im here to convince you today that that is a crying shame because theres a lot that this thing can teach us not just about geometry but about abstract algebra as well todays topic is the constructible numbers those are the numbers the lengths if you will that we can construct using just one of these a compass and one of these a straightedge notice this is a straightedge it doesnt have any markers on it its not a ruler its just a straight line youll have to imagine that its infinitely long but nevertheless were going to look at the numbers t