I took an abstract algebra course in college. I don't think we talked about squaring the circle, but we did visit the problem of trisecting the angle. What we l

I took an abstract algebra course in college. I don't think we talked about squaring the circle, but we did visit the problem of trisecting the angle. What we learned is that compass-straightedge construction can execute a finite number of primitive operations, notably the arithmetic operators +, -, *, and /, along with square root. And that's it. Then we showed that trisecting the angle requires a cube root button, which is what makes it impossible. The cool thing was finding a correspondence between geometry and algebra, followed by completing the proof as an almost trivial algebra problem.