Tudor M.

asked • 01/26/16

Fibonacci: other golden ratios for higher numbers?

I just want to know what this property that I'm about to show is called. So I'm not a mathematician and this may sound dumb :) but I was looking over a Fibonacci article yesterday and studied it's properties and I wondered: Well, if 1 has the golden ratio of 0.618 what if 2 has a certain golden ratio and 3 has one. And through trial and error I came up with this numbers that have the same properties analogous to the 1 and 0.618. For example:

For 2 I found: 2/0.732≈2.732
For 3: 3/0.7913≈3.7913

Now what I found was that these numbers share similar properties. For example:


Another one would be:


And another one:


I didn't test for other properties cause I think it's enough to make a point. So then I thought that there has to be a string of numbers to have same properties as the Fibonacci with 0.618 ratio.

So I realized that for:

0.732 it's 2 4 12 32 88 240 656 1792... Basically Fn=2(Fn−1+Fn−2)Fn=2(Fn−1+Fn−2)
And if you divide 1792/656 you get 2.732. If you divide 656/1792 you get approx 0.366 which times 2 is 0.732.

Same for 0.7913 it's 3 9 36 135 513 1944 7371 formula being Fn=3(Fn−1+Fn−2)Fn=3(Fn−1+Fn−2)
And same if you divide 7371/1944 you get approx 3.7913. And if 1944/7371 you get approx 0.2637 which times 3 is approx 0.7913.

Now what I want to know is what are these numbers or this property of numbers called? I looked for these ratios but didn't find anything.

3 Answers By Expert Tutors


Michael F. answered • 01/26/16

Mathematics Tutor

Cindy K. answered • 01/26/16

Top 1% Tutor Simplifies Lightroom, Excel and Business Analytics

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