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What is the formula for this recursive pattern?

  1. Mar 22, 2010 #1
    Hey what is the formula for this recursive pattern?

    http://img440.imageshack.us/img440/7528/recursion.jpg [Broken]

    It looks shocking & I would bet that there is a name for it.

    Perhaps it's a theorem or something?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 22, 2010 #2

    CompuChip

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    What do you want a formula for?
    The sides of the hypothenuses? The area of the triangles? The total area of the first n?
     
  4. Mar 22, 2010 #3
    Sorry, the fact that each hypoteneuse is an interger higher than the last hypoteneuse & that the leg is the previous hypoeneuse.

    It's just a crazy pattern that I've never seen before, I seen it in a book and it just looks awesome, is there some explanation?
     
  5. Mar 22, 2010 #4

    Dick

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    You can find the lengths of successive hypotenuses by using the Pythagorean theorem. If that's what you mean.
     
  6. Mar 22, 2010 #5
    Yeah I know, I do mean that, but it's the kind of thing a number theorist or somebody would make into a theorem (or probably already has).

    It's just amazing, I mean look at the pattern that emerges. That thing could probably go on to infinity, sprouting smaller and smaller triangles - kind of like a fractal.

    I would have assumed that it is some theorem, or has some special name or something.

    Maybe I've just found my own personal Fibonacci sequence :rofl:

    ___The_Pythagorasequence___
     
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