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How did Pythagoras know that his theorem was true?
He created a proof.
which of the following reasons can be used for statement 3 of the proof of the exterior angle theorem?
triangle sum theorem
Sequence of steps that leads to a valid conclusion as for the theorem?
proof
Do theorems need to be proved?
By definition, a theorem is a proven statement- until a proof is made for a statement, it is not a theorem but rather a conjecture. Whether you need to be able to reproduce the proof of a known theorem is another matter. If you trust the prover, I think you can make use of a theorem without knowing the proof. However, studying the proof can give you valuable insights into what the theorem really means and how it might be used. Also, reading proofs made by other people can help you prove you own theorems and write them up coherently.
What is the answer for Fermat's Last Theorem?
Fermat's Last Theorem states that an + bn = cn does not have non-zero integer solutions for n > 2. Various mathematicians have worked on Fermat's Last Theorem, proving it true for certain cases of n. In 1994, Andrew Wiles revised and corrected his 1993 proof of the theorem for all cases of n. The proof is very complex.
