Ask HN: Pure Math Problem

Posted by nsomaru on Wednesday May 16, 2012 @11:29PM
from the ask-hn dept.

I'm reading A Course of Pure Mathematics, by G. H. (Godfrey Harold) Hardy – available free on Gutenberg. In the first chapter he presents the following problem (on rational numbers):

If λ, m, and n are positive rational numbers, and m > n, then λ(m^2 − n^2), 2λmn, and λ(m^2 + n^2) are positive rational numbers. Hence show how to determine any number of right-angled triangles the lengths of all of whose sides are rational.

I'm not asking the solution, but I'm not sure what he means by "any number of right-angled triangles"

( 6 comments | 2 points | on HN )

Re:Ask HN: Pure Math Problem by Someone on Thursday May 17, 2012 @10:56AM (#3987241)

"any number" means that you must be able to produce two triangles if asked for two, three if asked for three, four if asked for four, 7 trillion if asked for 7 trillion, etc. Effectively, you have to be able to generate infinitely many (technically: aleph-0) Pythagorean triangles.

Aside: I do not think that is a the nice problem, as there are way easier ways to generate aleph-0 such triangles (I think most mathematicians would agree the simplest is 3x,4x,5x for x in {1,2,...}) But that is not what this question is hinting at.

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Re:Ask HN: Pure Math Problem by benjdezi on Thursday May 17, 2012 @01:54AM (#3985663)

It probably means that you need to use the given postulates and known theorems about right-angled triangles to come up with a way or formula for generating such triangles.

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Re:Ask HN: Pure Math Problem by sesqu on Wednesday May 16, 2012 @11:43PM (#3985284)

I'm guessing it means you have to come up with a generative process that produces k such shapes for any k.

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Re:Ask HN: Pure Math Problem by ciceroqaz on Wednesday May 16, 2012 @11:30PM (#3985245)

should probably ask in Art of Problem Solving.

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Re:Ask HN: Pure Math Problem by nsomaru on Wednesday May 16, 2012 @11:52PM (#3985310)

I did a Google search, but I'm not able to come up with anything but a non-profit that doesn't seem like a QnA site. Please advise?

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Re:Ask HN: Pure Math Problem by amair on Thursday May 17, 2012 @05:12AM (#3986122)

think Pythagorean triples

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