Ventus Posted June 12, 2019 Share Posted June 12, 2019 So everyone knows that a^2+b^2=c^2, but is there a set of numbers where a^2+b^2=2c^2? How would one go about finding these different set of numbers? Link to comment Share on other sites More sharing options...
DrP Posted June 12, 2019 Share Posted June 12, 2019 2 hours ago, Ventus said: everyone knows that a^2+b^2=c^2 This is for the specific case of a right angled triangle with hypotenuse c. 2 hours ago, Ventus said: but is there a set of numbers where a^2+b^2=2c^2? Yes - but not presumably for a right angled triangle where a2+b2 always = c2 where c is the hypotenuse. Unless you define c = half the length of the hypotenuse or forget anything about right angled triangles. Link to comment Share on other sites More sharing options...
Ventus Posted June 12, 2019 Author Share Posted June 12, 2019 6 hours ago, DrP said: Yes - but not presumably for a right angled triangle where a2+b2 always = c2 where c is the hypotenuse. Unless you define c = half the length of the hypotenuse or forget anything about right angled triangles. Yes, if we completely disregard right angled triangles and just look at a, b, and c as isolated variables. Link to comment Share on other sites More sharing options...
uncool Posted June 12, 2019 Share Posted June 12, 2019 There are countably many triplets of integers (a, b, c) such that a^2 + b^2 = 2c^2. There's even a method to find them. Do you know how to find a triplet (a, b, c) such that a^2 + b^2 = c^2? Link to comment Share on other sites More sharing options...
mathematic Posted June 12, 2019 Share Posted June 12, 2019 (edited) 14 minutes ago, uncool said: There are countably many triplets of integers (a, b, c) such that a^2 + b^2 = 2c^2. There's even a method to find them. Do you know how to find a triplet (a, b, c) such that a^2 + b^2 = c^2? a=2mn, b=m^2-n^2,c=m^2+n^2 Edited June 12, 2019 by mathematic typo Link to comment Share on other sites More sharing options...
uncool Posted June 12, 2019 Share Posted June 12, 2019 Do you know why that formula works, in a geometric sense? (I don't plan to simply give an answer at the moment; simply giving an answer is uninformative, and someone recently asked the same question in the Homework Help section) Link to comment Share on other sites More sharing options...
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