I made this map of the Pythagorean triples the other day (15/8/17) using this formula (Euclid). The triangles are scaled with hypotenuse=1pic.twitter.com/tCTpzLsyGR
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Just discovering this. This generation method doesn't provide all the pythagorean triples, right? For example, there's no m,n values for 9-12-15. The Euclid formula is mostly used to find primitive triples.
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Hmm can ne one explain this?
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Another proof: there are infinitely many triangles that are scales of the 3-4-5 one.
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Fermat's last tweet?
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a²+b²=c², a,b,c∈ℕ Pythagorean triple. Can be generated by Euclid's formula. m>n,∈ℕ, a=m²-n², b=2mn, c=(m+n)²-b; a&b=catheti, c=hypotenuse.
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Wouldn't it be 2(ab)^2, not (2ab)^2 ? Doesn't that invalidate this attempted proof?
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Love your tweet proofs. Keep 'em coming. :)
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