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Diff — Pythagorean triple

Revision #3197 → #3710 · back to history

modified(3, 4, 5) is a Pythagorean triplef48b4d435e58
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noteNo standalone lemma instantiating `PythagoreanTriple 3 4 5` was found.No standalone lemma instantiating `PythagoreanTriple 3 4 5` was found in `Mathlib/NumberTheory/PythagoreanTriples.lean`.
modifiedScaling a Pythagorean triple2f98112bb10a
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note`PythagoreanTriple.mul` shows scaling by `k` preserves the triple; `mul_iff` gives the iff form.`PythagoreanTriple.mul` shows scaling by `k` preserves the triple; `mul_iff` gives the iff form for nonzero `k`.
addedParity in primitive triple (odd square ≡ 1 mod 4)91f1a1b8475c
modifiedHypotenuse form 4n+1fd10a1207685
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noteSum-of-two-squares facts (`Nat.Prime.sq_add_sq`, `Nat.eq_sq_add_sq_iff`) give the general result; not specialized to hypotenuses.Sum-of-two-squares facts (`Nat.Prime.sq_add_sq`, `Nat.eq_sq_add_sq_iff`) give the general result; not specialized to Pythagorean hypotenuses.
modifiedAcute angles not rational degreesc7d1d1109639
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noteNiven-type irrationality of Pythagorean angles is not formalized.Niven's theorem on rational values of trig functions is not currently formalized as a Mathlib lemma applicable to Pythagorean angles.
addedPick's theorem (used for lattice triangle area)5e413e261b83
modifiedNo isosceles Pythagorean triplesa2458e354c22
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mathlib.declirrational_sqrt_two
mathlib.moduleMathlib.NumberTheory.Real.Irrational
noteFollows from irrationality of √2; not stated as a Pythagorean-triple lemma in Mathlib.Follows from irrationality of `√2` (`irrational_sqrt_two`); not stated as a Pythagorean-triple lemma in Mathlib.
statusnot_formalizedpartial