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It’s an abstraction that helps mathematicians study interesting phenomena. I believe the famous squaring the circle problem was resolved using the language of f
by markisus 1y ago
It’s an abstraction that helps mathematicians study interesting phenomena. I believe the famous squaring the circle problem was resolved using the language of fields.
- btilly 1y agoThat we can't square the circle comes from pi being transcendental. The result that you're thinking of is Galois' proof that there is no algebraic formula forroots of 5th degree polynomials.
- mathgradthrow 1y ago"transcendental" is field language
- btilly 1y agoI've always thought of "transcendental" as number theory language, though I can see how someone could argue that it is field language. But the Galois group of a field extension definitely is field language.
- mathgradthrow 1y agoa field extension is the thing which is transcendental or not.
- cka 1y agoYeah, and constructability is usually handled by proving that a length is constructable if it lives in an iterated quadratic extension of the rationals. Pi does not lie in such an extension, so is not a constructable length (and neither is its square root).