Fibonacci, Music and Skating

dont laugh, Even fibonacci proof seems mush easier.I wonder if egyptians could figure out jump rules/marks or Cop would make them wanna jump off the pyramids, pretty much what happens also to the average fs fan.

seniorita said:

dont laugh, Even fibonacci proof seems mush easier.I wonder if egyptians could figure out jump rules/marks or Cop would make them wanna jump off the pyramids, pretty much what happens also to the average fs fan.

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- :chorus:

Are you always this funny when you are sleep deprived?

Seriously though, I think Mishin has the secret of the Golden ratio.
Human genetics are based on this Golden ratio. That is what scientists follow for cloning. That finaly explains this "mini-Plushenko to me.
Even the nose of mini- Plushenko is an exact replica of original Plushenko. That could only be possible through cloning and Golden ratio.

janetfan said:

Seriously though, I think Mishin has the secret of the Golden ratio.
Human genetics are based on this Golden ratio. That is what scientists follow for cloning. That finaly explains this "mini-Plushenko to me.

Even the nose of mini- Plushenko is an exact replica of original Plushenko. That could only be possible through cloning and Golden ratio.

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Mishin has a "magic vest"

Someone has already mentioned the impact of Plushy's nose in balancing during jumps

janetfan said:

Does the Fibonacci sequence occur in, or apply to figure skating?

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Hmmm, good question. Thanks for giving me an idea for my thesis!

janetfan said:

- :chorus:
Even the nose of mini- Plushenko is an exact replica of original Plushenko. That could only be possible through cloning and Golden ratio.

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I know you enjoy the mini plushy clone thing but artur's nose is quite cute and in general i dont see much resemblance with plush on ice or off ice. The bad thing with that boy is that everyone expected him to be plushenko No2 from his 14 years and that put pressure on him, maybe he will blossom later.
Here is 2008 exhibition of arthur skating to adagio , i think he is more artistic skater than plush and naturally more cop friendly http://www.youtube.com/watch?v=zb3pN1zYNJA

hey mm you deleted your students paper? I was about to have an eye on it, I had an interesting conversation in the morning about egyptian maths

seniorita said:

hey mm you deleted your students paper? I was about to have an eye on it, I had an interesting conversation in the morning about egyptian maths

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I think you have to subscribe to the journal in order to read it on line. You can probably access it from a university network, since most universities subscribe. (The Fibonacci Quarterly is kind of a niche journal, as the name suggests.)

If you Google the author's name you can find the actual thesis itself, which is longer but much easier to read because it contains more expository material. This, however, also is available only through inter-university llibrary loan. We wrote up a version of the results for the lay audience and submitted it to Scientific American (a pop science magazine widely read in the U.S.), but it was not accepted for publication. (Oh well, like Sasha in the Grand Prix, I already have tenure. )

About the Egyptians, I think it is a stretch of the evidence to conjecture that they knew or cared anything about the golden ratio. Thousands of documents have been preserved from dynastic times, but only four have any real mathematical content, the most famous being the Ahmose, or Rhind, papyrus.

The relative dimensions of the pyramids were determined by a ratio called the seked -- what we now call the cotangent. The great pyramids had a seked of either five palms one finger or five palms two fingers. This means that the pyramid rises one royal cubit in height for every 5.25 or 5.5 palms in horizontal distance.

A royal cubit was 7 palms, so this gives a raio of 7/5.25 = 1.333 -- somewhat smaller than the golden ratio (sqrt(5)+1)/2 = 1.618.

(Now you are probably wondering why the royal cubic was so big. The Pharaoh, being a god, naturally had longer forearms than anyone else. A cubit is the distance from your elbow to the tip of your fingers. The common cubit, which was used in Egypt for less grand construction projects than the great pyramids, was 6 palms, which is about right, if you measure your cubit agains your palm. (A "palm" is four fingers -- don't count your thumb. ) Etymology: Latin "cubitum = elbow," from the Latin root word for "lying down," the idea being that the Romans reclined on their elbows for feasts).

Mathman said:

About the Egyptians, I think it is a stretch of the evidence to conjecture that they knew or cared anything about the golden ratio. Thousands of documents have been preserved from dynastic times, but only four have any real mathematical content, the most famous being the Ahmose, or Rhind, papyrus.

The relative dimensions of the pyramids were determined by a ratio called the seked -- what we know call the cotangent. The great pyramids had a seked of either five palms one finger or five palms two fingers. This means that the pyramid rises one royal cubit in height for every 5.25 or 5.5 palms in horizontal distance.

A royal cubit was 7 palms, so this gives a raio of 7/5.25 = 1.333 -- somewhat smaller than the golden ratio (sqrt(5)+1)/2 = 1.618.
)

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Thanks for sharing that information. I am sure seniorita will be glad to hear 1.6 belongs to the Greeks afterall.
Spirals were mentioned before - but is there anyway to explain Caroline's "pearl" position? Would pi be more applicable than phi - since her bending ability seems to be infinite?
(Sorry if that is too dopey - I should have taken more math courses back in the day.)

i asked them in the morning about our last night conversation and they didnt know about fibonacci and egyptians thats why i was curious to see it, the conversation ended up talking about their approach to π along with indians, which looked easier for skating relation
what you mean niche journal?
Thanx for info I will find a way to search now I m free for the summer

seniorita said:

i asked them in the morning about our last night conversation and they didnt know about fibonacci and egyptians thats why i was curious to see it, the conversation ended up talking about their approach to π along with indians, which looked easier for skating relation.

what you mean niche journal?

Thanx for info I will find a way to search now I m free for the summer

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Here is a good way to determine the value of π. Take a string as long as you are tall. Now wrap it around your head. How many times does it go around? About 3.14? :yes:

By the way, the value of π in the real world depends on the curvature of space-time. If space is positively curved, then π is slightly smaller than 3.14159..., and if space is negatively curved, then π is slightly greater than the Euclidean value.

One way that cosmologists try to determine the curvature of the universe is by computing the ratio of the surface area to the radius of large imaginary spheres, using information from distance quasars and supernovae.

By a "niche journal" I mean one that is dedicated to one particular narrow topic -- Fibonacci numbers, in this case -- rather than a general mathematics journal that publishes papers on a broad spectrum of topics.

If you seriously want to learn something about Egyptian mathematics you could start with primary documents such as the Rhind (Ahmose) Mathematical Papyrus. Assuming that you don't read the archaic Coptic language , there is an excellent translation into English by Robins and Shute, complete with photocopies of the document itself.

Ahmose (Ahmes) was the Egyptian scribe whose copy (16th centruty B.C.) has come down to us. Rhind was the rich British traveller who acquired the document from 19th century A.D. grave robbers and bequeathed it to the British Museum.

If you can't find the article that I referenced, here is another one (by three more of my students ) on a similar theme.

http://www.ams.org/mcom/2000-69-229/S0025-5718-99-01088-1/home.html

janetfan said:

Spirals were mentioned before - but is there anyway to explain Caroline's "pearl" position?

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Hmmm...

http://ocw.mit.edu/OcwWeb/Mathematics/18-034Spring-2007/CourseHome/

http://web.icenetwork.com/images/2007/11/08/RfaMqwn3.jpg

Mathman said:

Hmmm...

http://ocw.mit.edu/OcwWeb/Mathematics/18-034Spring-2007/CourseHome/

http://web.icenetwork.com/images/2007/11/08/RfaMqwn3.jpg

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I haven't read anything from first link - but did look at the pic and even inverted it's position.
Actually, there is an uncanny resemblance between that image and Caroline's pearl position. I am curious at the moment to see if I can find more specific infos about Mozart's use of the fibonacci sequence.
I may read from the Math link later this afternoon as it is both interesting and baffling to me.

Since the original post asked about skating examples,

Mathman said:

Hmmm...

http://ocw.mit.edu/OcwWeb/Mathematics/18-034Spring-2007/CourseHome/

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This is a good example of a "spiral" in the sense the word was originally used in skating -- an edge held on a diminishing curve that spiraled in toward a center, regardless of body position.



I don't know whether there is any association with the Fibonacci series or other special numbers that have been discussed in this thread, but here's a mathematical figure that is related to school figure loops:
http://www-groups.dcs.st-and.ac.uk/~history/Curves/Limacon.html

Scroll to the bottom for diagrams of what the figures were supposed to look like, and see FSR 1.14 on the third page for details of what the dimensions were supposed to be:
http://www.oregonskating.org/docs/Announcements/FiguresRegs.pdf
(I don't think the diagrams match the descriptions)

gkelly said:

...here's a mathematical figure that is related to school figure loops:

http://www-groups.dcs.st-and.ac.uk/~history/Curves/Limacon.html

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Very cool. If you click on the java applet "HERE" and set the polar parameters to b=1 and a = ,5 you get the perfect cartoid (heart).

Scroll to the bottom for diagrams of what the figures were supposed to look like, and see FSR 1.14 on the third page for details of what the dimensions were supposed to be:

http://www.oregonskating.org/docs/Announcements/FiguresRegs.pdf

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To me, the most visually striking thing about these pictures is that they are all very round. Almost perfect circles, with little embellishments. Since the skater is going slowly enough that cetrifugal force does not play a role, it must be really hard to hold that edge so perfectly for the whole figure. In fact, I don't see how you can do it at all. What stops you from toppling over into the circle?

This example is kind of fun for it's visual effect.

http://www.missioncollege.org/depts/math/keller/gmean_3.html

janetfan said:

This example is kind of fun for it's visual effect.

http://www.missioncollege.org/depts/math/keller/gmean_3.html

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:agree: Is there any way you can hack that so it shows Caroline's pearl spin at the end?

Mathman said:

:agree: Is there any way you can hack that so it shows Caroline's pearl spin at the end?

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Great idea - but that would exceed by about 98% my computer skills.

But honestly, from the earlier example you used I did see it. I am not sure if I interpret it correctly but Carolines layback shows me the human body is based on the Golden ratio. Or atleast Sweet Caroline's body is
On the other hand I think certain pics of Caroline should come witht he same warning you mentioned about Shizuka's Ina Bauer. "Don't try this at home......

Here is a nice link to Da Vinic's "Vitruvian Man"

http://arthistory.about.com/library/weekly/bl_leo_vitruvian_man.htm

I bet this Vitruvian dude would have been some great jumper - better even than Plushy

Assuming that you don't read the archaic Coptic language

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this is the book? http://www.amazon.co.uk/Rhind-Mathematical-Papyrus-Ancient-Egyptian/dp/0486264076/ref=sr_1_2?ie=UTF8&s=books&qid=1244572529&sr=1-2

I havent actually known much about history of mathematics in theory apart from the very important ones starting from hellenistic period, so that would be fun

i had read about the compose of music using hailstone sequences , but i dont know how.

You want this caroline image?http://web.icenetwork.com/images/2007/11/08/RfaMqwn3.jpg
You have a better one ?

janetfan said:

Here is a nice link to Da Vinic's "Vitruvian Man"

http://arthistory.about.com/library/weekly/bl_leo_vitruvian_man.htm

I bet this Vitruvian dude would have been some great jumper - better even than Plushy

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Actually, if was truly Da Vinci's intention to try to square the circle, but not let anyone know he was doing so because of his reverence for John the Baptist -- hey, that would make a good movie! -- this is in the same spirit as a proof by Archimedes, based on his golden (logarithmic) spiral that in fact works exactly. (It does not solve the classical ruler-and-compass problem, because you have to use your instruments in a funny way to construct the spiral in the first place.)

http://www.gap-system.org/~history/HistTopics/Squaring_the_circle.html

(Scroll about halfway down the page for Archimedes' construction.)

yesterday , i think in one of the links janetfan or you gave, it was written that although people think davinci used the golden ratio to draw the vitruvian man, actually he didnt. Did he?
You didnt give me a good photo of caroline for your pearl request so i made you this, I hope you can see .swf
http://www.mediafire.com/?omn2ujjvmtm