Fibonacci, Music and Skating

[janetfan]

Hmmm...

http://ocw.mit.edu/OcwWeb/Mathematic...07/CourseHome/

http://web.icenetwork.com/images/200...8/RfaMqwn3.jpg

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.

[gkelly]

Since the original post asked about skating examples,

Hmmm...

http://ocw.mit.edu/OcwWeb/Mathematic...07/CourseHome/

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/~...s/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/An...iguresRegs.pdf
(I don't think the diagrams match the descriptions)

[Mathman]

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

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

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/An...iguresRegs.pdf

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?

[janetfan]

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

http://www.missioncollege.org/depts/...r/gmean_3.html

[Mathman]

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

http://www.missioncollege.org/depts/...r/gmean_3.html

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

[janetfan]

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

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......

[janetfan]

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

http://arthistory.about.com/library/...ruvian_man.htm

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

[seniorita]

Assuming that you don't read the archaic Coptic language

this is the book? http://www.amazon.co.uk/Rhind-Mathem...4572529&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/200...8/RfaMqwn3.jpg
You have a better one ?

[Mathman]

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

http://arthistory.about.com/library/...ruvian_man.htm

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

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/H...he_circle.html

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

[seniorita]

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

[Mathman]

this is the book? http://www.amazon.co.uk/Rhind-Mathem...4572529&sr=1-2

Yes. The actual text looks like this.

http://thelongestlistofthelongeststu...ges4/rhind.JPG

Can you find a mistake on this page? (It says 7 to the 5th power is 16707 insread of 16807. )

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

You mentioned Imdian mathematics before. In trigonometry, the word "sine" is taken from the Sanskit word for "bowstring."

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

I can't imaging how this would sound. These sequences are all but random, until the last few notes. It would be like a kitten bouincing about on the piano keys.

You want this caroline image?

http://web.icenetwork.com/images/200...8/RfaMqwn3.jpg

You have a better one ?

That's the best I've seen yet.

[Mathman]

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

OK, first -- You know how to make swf files?! Now I am really impressed!

EVERYBODY DOWNLOAD THIS!

[janetfan]

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

Thanks so much seniorita. Your example is great - better than just using a picture. My download was easy, no problems.
I really, really like it and appreciate it it very much.
In case you don't know I love "Princess Caroline.
Dont worry, you are better

[seniorita]

Now you are impressed?
(joke)

Yes. The actual text looks like this.

http://thelongestlistofthelongeststu...ges4/rhind.JPG

Can you find a mistake on this page? (It says 7 to the 5th power is 16707 insread of 16807. )

I hope you kid

I can't imaging how this would sound. These sequences are all but random, until the last few notes. It would be like a kitten bouincing about on the piano keys.

I m talking nonsense? I think about this sequence with odd and even numbers, since next number will be either half or 3 times the previous one, you pass the numbers through logarithmic fuction of ten, the fact that last numbers repeat themselves was like closing the music piece, and you get something that sounds like this http://www.mediafire.com/?myooydwiwom
i dont get any credit for this, i had read this all on a site or something when we were trying to simulate a h. sequence a month ago.

[janetfan]

Here is a puzzle using the knight piece from chess. Something also about the knight using the the fibonacci numbers when it moves 2+1 or 1+2

http://www.borderschess.org/KnightTour.htm

I was reading a few articles about disclaimers for the Golden Ratio. Mostly about music and saying it's use by Mozart in particular may be more accidental than intentional. He did write many piano sonatas (two movements in his era) and many of them switch from 1st to 2nd movement at 62nd measue, leaving 38 measures for 2nd mvt.
If anyone can complete the chess puzzle let us know.
I tried the puzzle once - and although i did poorly, oddly enough, i left 13 open.