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#1 2013-02-08 04:20:24
- Norvegicusbass
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Help understanding this
While reading about calculating the perimeter of an ellipse on the Math Is Fun website I came across a formula that I just dont understand. I am sorry that I cant seem to upload an image of the formula but its titled Infinite Series 2 and the author quotes it as being their favourite method. Thing is I dont understand how the thing breaks down in laymans terms. It has Binomial Coefficients and Factorials of Half Integers which I dont follow. Infact when I try to use my calculator to work out half integer factorials it doesnt work! I dont understand how you arrive at the numbers that you plug into this equation to obtain the answer. Because of the ruling that only established members can post links I cant show you a link to the page but it is on the Math Is Fun site.
Thank you all in advance for your time.
Last edited by Norvegicusbass (2013-02-08 04:21:59)
#2 2013-02-08 04:43:11
- bob bundy
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Re: Help understanding this
hi Norvegicusbass
Welcome to the forum.
http://www.mathsisfun.com/geometry/elli … meter.html
hhmmm! Got me beat as well. Luckily there are some really clever mathematicians on the forum who will be able to tell you. 
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#3 2013-02-08 04:49:50
- anonimnystefy
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Re: Help understanding this
Hi
The binomial of half integers is based on the extension of the factorial to the gamma function.
There is a lot of information about it on the Wiki page for factorial.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#4 2013-02-08 05:02:14
- zetafunc.
- Guest
Re: Help understanding this
I've never seen those formulae on that page, but they do look quite interesting. Fractional factorials can be more readily computed using the gamma function, defined as:
with .
As for the calculation of the perimeter of an ellipse... well, my first thought was just to say
General form of an ellipse:
Clearly,
but the arc length of a function is given by
and we get
here I use the substitution x = asinθ and end up with
which doesn't seem to help at all and looks like I've just written the ellipse in parametric form! And I am stuck here... can anyone help?
(Is this where the famed 'elliptic integrals' come from...?)
#5 2013-02-08 05:07:40
- zetafunc.
- Guest
Re: Help understanding this
You can get the perimeter of a circle easily in that integral setting a = b = 1, but for differing a and b, I am stuck.
#6 2013-02-08 05:13:15
- anonimnystefy
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Re: Help understanding this
Hi zf.
The circumference of the ellipse is connected to the complete elliptic integral of second kind. You can check the Wiki page for the ellipse, if you want.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#7 2013-02-08 05:17:59
- zetafunc.
- Guest
Re: Help understanding this
anonimnystefy wrote:
Hi zf.
The circumference of the ellipse is connected to the complete elliptic integral of second kind. You can check the Wiki page for the ellipse, if you want.
Thanks for confirmation! I just entered some random values for a and b in for WolframAlpha and it came up with that too...
#8 2013-02-08 05:22:53
- anonimnystefy
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Re: Help understanding this
It's too bad that there is no exact closed formula for the ellipse circumference...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#9 2013-02-08 20:08:31
- Norvegicusbass
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Re: Help understanding this
Thank you all for your replies. but can anyone show me how the numbers get put into this equation? I often need to see a worked example to get the feel for how these formulas work otherwise they leave me a little confused ( I am not a mathematician LOL ). I mean on that site it shows you the expansion as
1+ h/4 + h²/64 + h³/256... so why is the next term 25h4/16384?? instead of h4/1024? So I guess what I am asking is when a mathematician sees the formula we are discussing they can use it as a kind of instruction and arrive at definate answer using real numbers and plugging them in whereas I havent got a clue how the numbers are arrived at. Is there a site where worked examples are given?
BTW sorry about using a lower case 4 in place of a raise in power I copied and pasted it and couldnt get it to look right:P
#10 2013-02-08 20:15:01
- anonimnystefy
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Re: Help understanding this
Hi Norvegicusbass
Try calculating the values of
using Wolfram Alpha (link).
Last edited by MathsIsFun (2013-02-11 17:27:58)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#11 2013-02-11 10:55:16
- Norvegicusbass
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Re: Help understanding this
Yeah but even this makes little sense to me. Imagine a person you needed to explain in kindergarden language a particular mathematical term to. That person is me. Take it as a personal challenge to explain to someone dumb as me and you will cover yourself in the glory of what it is to be a true educator
#12 2013-02-11 22:23:31
- bobbym
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Re: Help understanding this
1+ h/4 + h²/64 + h³/256... so why is the next term 25h4/16384?? instead of h4/1024?
To answer that we would have to take a look at how the formula is derived.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.