What is the formula for this recursive pattern?

[sponsoredwalk]

Hey what is the formula for this recursive pattern?

http://img440.imageshack.us/img440/7528/recursion.jpg

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

Perhaps it's a theorem or something?

 

[CompuChip]

What do you want a formula for?
The sides of the hypothenuses? The area of the triangles? The total area of the first n?

 

[sponsoredwalk]

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?

 

[Dick]

You can find the lengths of successive hypotenuses by using the Pythagorean theorem. If that's what you mean.

 

[sponsoredwalk]

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

___The_Pythagorasequence___