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# Pythagorean Triples

Started by BMAD, Jul 19 2013 05:46 PM

6 replies to this topic

### #1

Posted 19 July 2013 - 05:46 PM

The most famous Pythagorean Triangle (a right triangle with all integer sides) is the 3 , 4 , 5 where 3^2 + 4^2 = 5^2. The 'legs', a=3 and b=4, are

consecutive integers, making a nearly-isosceles right triangle. What are the next two smallest integral right triangles with consecutive legs?

### #2

Posted 19 July 2013 - 07:16 PM Best Answer

Spoiler for

### #3

Posted 19 July 2013 - 08:31 PM

Spoiler for how about

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #4

Posted 19 July 2013 - 08:53 PM

Spoiler for how about

Hmm do they consider the hypotenuse a leg in America?

### #5

Posted 19 July 2013 - 08:53 PM

I've exhausted all triangles whose two legs differ by 1 where

the length of the shortest leg is less than or equal to 10

I found only 9:

3 4 5

20 21 29

119 120 169

696 697 985

4059 4060 5741

23660 23661 33461

137903 137904 195025

803760 803761 1136689

4684659 4684660 6625109

the length of the shortest leg is less than or equal to 10

^{10}.I found only 9:

3 4 5

20 21 29

119 120 169

696 697 985

4059 4060 5741

23660 23661 33461

137903 137904 195025

803760 803761 1136689

4684659 4684660 6625109

### #6

Posted 20 July 2013 - 04:48 AM

Spoiler for how about

Hmm do they consider the hypotenuse a leg in America?

No, they don't.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #7

Posted 20 July 2013 - 05:22 AM

Spoiler for further proof

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