# Thread: Fibonacci, Music and Skating

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## Fibonacci, Music and Skating

Does the Fibonacci sequence occur in, or apply to figure skating? It seems to be relevant to many things in our universe. They appear in our genetic code, and in plant and animal life. Western music is based on them (a natural occurance heard simpy by plucking a guitar string) first applied by JS Bach and playfully used by Mozart in some of his compositions. Bartok also used them.
Just wondering if much about skating - jumps in particular - can be measured or if the mass/force ratio needed in jumps have any relationship to this sequence.
Maybe Doctor Mishin is aware of them If jumps are a natural act then the sequence might occur - if they are an unatural act in a physical sense then the sequence probaly would not apply. It could also explain why it is so hard for skaters to master triple jumps. Or maybe neither applies.

Poems have been written using this sequence, they even play a part in "The Da Vinci Code" "Angels and Demons" and other contemporary novels.

In music the 1,3,5 notes/tones are the key notes within a scale. A complete major scale consists of 8 notes and an octave consists of 13 half steps/tones. All Fibonacci numbers. Violins are designed on the Fibonacci numbers.

Please feel free to answer or ignore this message but as silly as it sounds any insights would be appreciated.

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What exactly is a Fibonacci sequence?

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Or even Golden skate forum is following fibonacci sequence à la golden ratio

Fibonacci's golden analogy is said to be discovered long before Fibonacci himself, by ancient greeks and the Parthenon actually fits in the golden rectangle

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Mathman can explain them better but basically it is a sequence of numbers that are found everywhere and in mnay things.

1+1 = 2, 2+1 = 3, 3+2 = 5, 5+3 + 8, 8+5 =13, 13+8 = 21 and on into infinity.

Believe it or not, this sequence appears in all life, even in genetic coding of plants, animals and humans. It also applies to non-organic things like the vibrating of a guitar string.

If you are interested - do a quick search - there are hundreds of webpages on the Fibonaci numbers.
I am not a mathematician but have a layman's interest in math. As a musician the sequence is very interesting to me, but if serious math "geeks" were discussing them it would be like Greek to me.

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Originally Posted by seniorita
Or even Golden skate forum is following fibonacci sequence à la golden ratio

Fibonacci's golden analogy is said to be invented long before Fibonacci himself, by ancient greeks and the Parthenon actually fits in the golden rectangle

Muchas gracias seniorta, si, si es verdad.
Yes, the Golden ratio and the number phi are related.
I just saw a documentary about the building and design techniques of the Parthenon and it was amazing. I believe the Pyramids of Egypt are also based on the Golden ratio.
I also wonder if Mishin has taught this to Plushy. How else can one explain those magical quad jumps

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Fibonacci sequence is based on the rule that each number is created by the sum of previous too. Nature follows it in many examples as janet said, from plants and animals to our own finger parts and it maximizes the growing of things in a certain space without losing their shape. (This is not official regulation it is my mind's one)
Golden analogy symbolized with the greek letter φ is the 1.61 analogy of the one number and the previous one in Fibonacci sequence (5/3, 8/5 etc) and is met even on your face analogy.
Ok mathman can sayall this better, seriously and official
I cannot think about jumps anything right now but i can think of the golden alalogy being applied to a perfect spiral.

off topic I know why it must be confusing but I m not spanish seniorita is a song i liked a lot by James english band and was listening to it when i signed up
I m greek

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Originally Posted by seniorita
Fibonacci sequence is based on the rule that each number is created by the sum of previous too. Nature follows it in many examples as janet said, from plants and animals to our own finger parts and it maximizes the growing of things in a certain space without losing their shape. (This is not official regulation it is my mind's one)
Golden analogy is the 1.61 analogy of the one number and the previous one in Fibonacci sequence and is met even on your face analogy.
I cannot think about jumps anything right now but i can think of the golden alalogy being applied to a perfect spiral.

off topic I know why it must be confusing but I m not spanish seniorita is a song i liked a lot by James english band and was listening to it when i signed up
I m greek

I thought you might be from Siberia - are you really Greek? I wanted to ask you someday if you have ever been to Lake Baikul - my dream destination !
I thought about changing my name here - I am a guy and a fan of Janet Lynn = "janetfan."
Back to the topic - you mentioned the the facial proportion - but this is not always true. Just look at Plushy's nose and we see the Golden proportion is not working there :laugh :
Back to real topic - How might a spiral be an example of Golden Ratio/Fibonacci Sequence? And there are many different spirals. Sasha and Caroline's seem "more perfect" than most other skaters.

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I dont even know this lake!From Siberia?Come on, since you read the plushenko thread, have you notice I dont know any russian word and usually news come from google translation?I havent actually expressed any special love for russian skaters, just some happen to be among my favs Yes, lol, i m really just a greek girl, sorry to disappoint you!

Actually nose size in length is not important, golden analogy applies on the human face not this way, if you draw perfect rectungle around the face, it applies on the distance between the eyes and the place of nose and mouth and the distance between eyes and chin, and the width of mouth should be φ times bigger than width of nose, something like that, argg i m not a plastic surgeon!

lol sorry i called you again janet, you can see names can be confusing!
As a musician the sequence is very interesting to me, but if serious math "geeks" were discussing them it would be like Greek to me.
well now you know i can help on that!
I havent heard the golden analogy about pyramids by the way. I m curious now.
There is a golden spiral in mathematics growing by the rules of golden ratio. lol, I was about to celebrate cause my exams finished today, now I see i need to revise again !

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Originally Posted by seniorita
I dont even know this lake!From Siberia?Come on, since you read the plushenko thread, have you notice I dont know any russian word and usually news come from google translation?I havent actually expressed any special love for russian skaters, just some happen to be among my favs Yes, lol, i m really just a greek girl, sorry to disappoint you!

Actually nose size in length is not important, golden analogy applies on the human face not this way, if you draw perfect rectungle around the face, it applies on the distance between the eyes and the place of nose and mouth and the distance between eyes and chin, and the width of mouth should be φ times bigger than width of nose, something like that, argg i m not a plastic surgeon!

lol sorry i called you again janet, you can see names can be confusing!
I havent heard the golden analogy about pyramids by the way. I m curious now.
There is a golden spiral in mathematics growing by the rules of golden ratio. lol, I was about to celebrate cause my exams finished today, now I see i need to revise again !
I picked up under your name "Tigre de Siberia" or something like that. Now it says "Return of The King." That, and fact you are always defending Plushy made me think you were a Siberian/Russian girl. Greek is fine - I love ouzo and Greek olives and still can't believe Greece won the Euro Cup in 2004 (?)
Baikul is the biggest lake in the world......in Siberia,,,,,,watch someday for a documentary about it - very interesting.
I don't know if you play piano but someday sit down and start at middle "C". Then begin to count the white keys using the Fibonacci sequence, playing each note after you have counted the sequence and you will see how it works in music. Then play the 1st, 3rd, and 5th white keys simultaneously - a C major chord - and you will hear sounds based on the sequence and the sound that western music is based on.
I think I read that the size of the stone blocks use to build the pyramids follows the the Golden ratio. How did they know this?

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The golden spiral, built up of "golden rectangles" whose sides are approximately the Fibonacci sequence.

http://www.sfecon.com/images/Whyperb/Spiral.gif

Here it is in nature.

http://www.world-mysteries.com/fib_nautilus2.jpg

Here it is in figure skating (Starts at the 3:35 minute mark. If you watch her lips you can see that she is counting the Fibonacci sequence backward )

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Originally Posted by janetfan
I picked up under your name "Tigre de Siberia" or something like that. Now it says "Return of The King." That, and fact you are always defending Plushy made me think you were a Siberian/Russian girl.
Tigre de Sibérie I heard it from french friends that call him like this and I liked it
Well ...you are always defending Plushy also , but I guess you are not also a Siberian/Russian girl.
and still can't believe Greece won the Euro Cup in 2004 (?)
.. and i used to like you here..it was one of the rare moments with extremely luck and guts and it wont happen in this century again, promise.
No piano, but i know reed organit goes simpler than this if you consider 8 notes in octave and 13 piano keys, all fibonacci nunbers

wow mathman does she really count???great spiral, michelbonacci!

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Originally Posted by Mathman

The golden spiral, built up of "golden rectangles" whose sides are approximately the Fibonacci sequence.

http://www.sfecon.com/images/Whyperb/Spiral.gif

Here it is in nature.

http://www.world-mysteries.com/fib_nautilus2.jpg

Here it is in figure skating (Starts at the 3:35 minute mark. If you watch her lips you can see that she is counting the Fibonacci sequence backward )

Thankyou mathman. I haven't seen that Gala by Michelle in ages. What warm memories it brings back!

Hmmm,,,,,,,what about the ratio between the length and height of a skating boot? Or the ratio between the length of the blade to the length of the boot? Boots are designed to provide the best natural glide - so I wonder if the Golden ratio might be used in boot design? It could be true whether or not the boot designers were aware of it,,,,,,,Stop chucking! - it's possible!

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If you want to check out the relation between Fibonacci numbers and the Egyption system of fractional arithmetic, here is a paper by a student of mine (the essential content of her master's thesis) that appeared in the Fibonacci Quarterly:

Mi-Kyung Joo, On the system of congruences Σ Π N/p = 1 mod(p), Fibonacci Quarterly, vol. 33. no. 3, pages 258-267,1995.

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Originally Posted by Mathman
If you want to check out the relation between Fibonacci numbers and the Egyption system of fractional arithmetic, here is a paper by a student of mine (the essential content of her master's thesis) that appeared in the Fibonacci Quarterly:

Mi-Kyung Joo, On the system of congruences Σ Π N/p = 1 mod(p), Fibonacci Quarterly, vol. 33. no. 3, pages 258-267,1995.

I will check it out - but it will be like GREEK to me. On the other hand it should be easy for seniorita to analyze it since she already understands Greek.....

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Originally Posted by janetfan
Hmmm,,,,,,,what about the ratio between the length and height of a skating boot? Or the ratio between the length of the blade to the length of the boot? Boots are designed to provide the best natural glide - so I wonder if the Golden ratio might be used in boot design? It could be true whether or not the boot designers were aware of it,,,,,,,Stop chucking! - it's possible!
I'm on it! Already I see that there are 13 hooks and eyes on a skating boot.

http://visual.merriam-webster.com/im...gure-skate.jpg

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