Brady Numbers - Numberphile
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Date: 2022-04-08
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Comments and reviews: 9
Aggelos
I was thinking of this about two months ago and I got very excited. I thought that if the Fibonacci sequence starting with 1 and 1 has this property, then it's probably because of the way the sequence is built and not because of the first two numbers. So I tried it with other starting numbers including negative numbers and I found that the property I'd true for every starting real numbers except if one of them is zero or they are the same.
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I was thinking of this about two months ago and I got very excited. I thought that if the Fibonacci sequence starting with 1 and 1 has this property, then it's probably because of the way the sequence is built and not because of the first two numbers. So I tried it with other starting numbers including negative numbers and I found that the property I'd true for every starting real numbers except if one of them is zero or they are the same.
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MalcolmCooks
-1, and then for no obviously explained reason another 1-
this has always bothered me about the fibonacci sequence
like, obviously the way the sequence is defined you have to start by setting the first 2 terms but its always annoyed me since almost every other sequence I have heard of only needs the first term to be set
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-1, and then for no obviously explained reason another 1-
this has always bothered me about the fibonacci sequence
like, obviously the way the sequence is defined you have to start by setting the first 2 terms but its always annoyed me since almost every other sequence I have heard of only needs the first term to be set
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SmileyMPV
Just saying, if negative irrational values are allowed, on very rare occasions, the ratio will not approach the golden ratio (1+sqrt(5)/2, but its brother (1-sqrt(5)/2. This happens if, and only if, the ratio of the first two terms is exactly (1-sqrt(5)/2. Also worth mentioning is the zero sequence where the ratio is undefined.
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Just saying, if negative irrational values are allowed, on very rare occasions, the ratio will not approach the golden ratio (1+sqrt(5)/2, but its brother (1-sqrt(5)/2. This happens if, and only if, the ratio of the first two terms is exactly (1-sqrt(5)/2. Also worth mentioning is the zero sequence where the ratio is undefined.
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technoway
My favorites sequence is this:
If P (short for Phi) is the Golden ratio, and x-y is x raised to the power y, then form the infinite sequence:
1, P, P-2, P-3, P-4, P-5, .
Every term is the sum of the previous two terms, and the quotient of any successive term divided by the previous term is (obviously) exactly P.
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My favorites sequence is this:
If P (short for Phi) is the Golden ratio, and x-y is x raised to the power y, then form the infinite sequence:
1, P, P-2, P-3, P-4, P-5, .
Every term is the sum of the previous two terms, and the quotient of any successive term divided by the previous term is (obviously) exactly P.
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GoldenKingStudio
-Often things in nature come in numbers, and some of those numbers are on this list. - I love the sarcasm there, I have the same opinion. But I have to say that the Fibonacci Numbers are important, because they are the simplest sequence, and are linked to Phi by Phi's continued fraction expansion.
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-Often things in nature come in numbers, and some of those numbers are on this list. - I love the sarcasm there, I have the same opinion. But I have to say that the Fibonacci Numbers are important, because they are the simplest sequence, and are linked to Phi by Phi's continued fraction expansion.
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Robin
what about the rate of convergence? is it always the same or are there some special pairs of initial values that maximize this rate? if that would be the case, then one might justifiably say that the association of the resulting sequence with the golden ratio is even stronger than for the fibonacci sequence.
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what about the rate of convergence? is it always the same or are there some special pairs of initial values that maximize this rate? if that would be the case, then one might justifiably say that the association of the resulting sequence with the golden ratio is even stronger than for the fibonacci sequence.
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Nisarg
hey, I did this method with different numbers and then I found out that the more there is difference between the first two no. the more nth terms will take to get number closer to golden ratio. Therefore I have a question that is the Fibonacci sequence the best sequence to get the golden ratio
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hey, I did this method with different numbers and then I found out that the more there is difference between the first two no. the more nth terms will take to get number closer to golden ratio. Therefore I have a question that is the Fibonacci sequence the best sequence to get the golden ratio
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Gabriel
I guess the special thing about the Fibonacci Sequence, besides the nature patterns, is that you can represent the Golden Ratio by putting squares with Fibonacci Numbers as their side lengths together, creating a nice looking rectangle with a nice looking spiral.
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I guess the special thing about the Fibonacci Sequence, besides the nature patterns, is that you can represent the Golden Ratio by putting squares with Fibonacci Numbers as their side lengths together, creating a nice looking rectangle with a nice looking spiral.
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Blake
However, the ratio of successive Fibonacci numbers is closer to the golden ratio relative to the denominator. As in if we have F_n/F_-n-1- you can't be any closer to the Golden ratio for any n < F_-n-1-. As F_n/F_-n-1- is its nth convergent.
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However, the ratio of successive Fibonacci numbers is closer to the golden ratio relative to the denominator. As in if we have F_n/F_-n-1- you can't be any closer to the Golden ratio for any n < F_-n-1-. As F_n/F_-n-1- is its nth convergent.
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