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        riddles >> easy >>  Pythagorean triple
        
(Message started by: LeoYard on Nov 23^rd, 2012, 8:16pm)

Title: Pythagorean triple
Post by LeoYard on Nov 23^rd, 2012, 8:16pm

Pythagorean triple (33, 56, 65)

hypotenuse = 65, side b = 56
the digits are reversed.

Can we find a similar situation with larger numbers?

Title: Re: Pythagorean triple
Post by towr on Nov 24^th, 2012, 2:04am

Yes, for example:
[hide]50160, 697996, 699796
2125530, 4364584, 4854634
2525490, 6262576, 6752626
[/hide]
I suspect there are infinitely many, because I see no reason why not. But brute force search hasn't yielded many, and none of them are primitive (which is another question).

Title: Re: Pythagorean triple
Post by towr on Nov 24^th, 2012, 2:20am

Actually, it should have been obvious we can just take the 33,56,65 triple, and multiple it by 10ⁿ+1 with n >1 (or similar repeating patterns). So just there's an infinite number of them already. Which makes searching for primitive triples the only really interesting part.

Title: Re: Pythagorean triple
Post by Christine on Jan 9^th, 2013, 10:50am

Given 3 Pythagorean triangles with the same hypothenuse, is it possible that the area of one triangle is equal to the sum of the areas of the other two triangles?

Title: Re: Pythagorean triple
Post by Annettagiles on Oct 13^th, 2014, 4:41am

Could you please explain me briefly I can't understand the question

Title: Re: Pythagorean triple
Post by towr on Oct 13^th, 2014, 8:54am

on 10/13/14 at 04:41:59, Annettagiles wrote:

Could you please explain me briefly I can't understand the question

What part of the question don't you understand?

Pythagorean triple (http://en.wikipedia.org/wiki/Pythagorean_triple)?
hypotenuse (http://en.wikipedia.org/wiki/Hypotenuse)?
digit (http://en.wikipedia.org/wiki/Numerical_digit)?

There is quite a lot that could need explanation depending on the level of understanding you're at. What's you're native language and level of education?

Title: Re: Pythagorean triple
Post by dudiobugtron on Oct 13^th, 2014, 11:34am

I don't really understand Christine's question either!

Quote:

Given 3 Pythagorean triangles with the same hypothenuse, is it possible that the area of one triangle is equal to the sum of the areas of the other two triangles?

What is a 'pythagorean triangle'?

Title: Re: Pythagorean triple
Post by towr on Oct 13^th, 2014, 11:49am

on 10/13/14 at 11:34:52, dudiobugtron wrote:

I don't really understand Christine's question either!

What is a 'pythagorean triangle'?

I'd assume it's a triangle formed by a Pythagorean triple.

Quote:

http://en.wikipedia.org/wiki/Pythagorean_triple
A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle.