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bobbym
2013-02-11 22:23:31

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.

Norvegicusbass
2013-02-11 10:55:16

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

anonimnystefy
2013-02-08 20:15:01

Hi Norvegicusbass

Try calculating the values of

Norvegicusbass
2013-02-08 20:08:31

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

anonimnystefy
2013-02-08 05:22:53

It's too bad that there is no exact closed formula for the ellipse circumference...

zetafunc.
2013-02-08 05:17:59

#### 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...

anonimnystefy
2013-02-08 05:13:15

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.

zetafunc.
2013-02-08 05:07:40

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.

zetafunc.
2013-02-08 05:02:14

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...?)

anonimnystefy
2013-02-08 04:49:50

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.

bob bundy
2013-02-08 04:43:11

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

Norvegicusbass
2013-02-08 04:20:24

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.