What is the formula for this recursive pattern?

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In summary, the formula for the recursive pattern shown in the given image is found by using the Pythagorean theorem to calculate the lengths of successive hypotenuses. This pattern is similar to a fractal and could potentially continue on to infinity. It may be considered a personal version of the Fibonacci sequence.
  • #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?
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  • #2
What do you want a formula for?
The sides of the hypothenuses? The area of the triangles? The total area of the first n?
  • #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?
  • #4
You can find the lengths of successive hypotenuses by using the Pythagorean theorem. If that's what you mean.
  • #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:


What is the formula for this recursive pattern?

The formula for a recursive pattern is a mathematical expression that describes how the pattern changes or repeats itself based on previous terms or values.

How do I find the formula for a recursive pattern?

To find the formula for a recursive pattern, you need to identify the pattern's starting value, the rule for how it changes or repeats, and the number of terms or values you want to find. Then, you can use algebraic techniques to derive the formula.

Is there a general formula for all recursive patterns?

No, there is no one-size-fits-all formula for recursive patterns. Each pattern is unique and may require different methods to find its formula. Some patterns may even have more than one possible formula.

Can recursive patterns be represented graphically?

Yes, recursive patterns can be represented graphically by plotting the values or terms of the pattern on a graph. This can help visualize the pattern and identify any trends or relationships between the values.

Do recursive patterns only involve numbers?

No, recursive patterns can involve numbers, letters, or other symbols. They can also appear in various contexts, such as in nature, language, or design. The important factor is that the pattern must follow a specific rule or logic for it to be considered recursive.

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