Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2013-02-07 05:20:24

Norvegicusbass
Member
Registered: 2013-02-07
Posts: 3

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 (2013-02-07 05:21:59)

Offline

#2 2013-02-07 05:43:11

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,259

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.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#3 2013-02-07 05:49:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

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.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#4 2013-02-07 06:02:14

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 2013-02-07 06:07:40

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 2013-02-07 06:13:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

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.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#7 2013-02-07 06:17:59

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 2013-02-07 06:22:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Help understanding this

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#9 2013-02-07 21:08:31

Norvegicusbass
Member
Registered: 2013-02-07
Posts: 3

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

Offline

#10 2013-02-07 21:15:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Help understanding this

Hi Norvegicusbass

Try calculating the values of


using Wolfram Alpha (link).

Last edited by MathsIsFun (2013-02-10 18:27:58)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#11 2013-02-10 11:55:16

Norvegicusbass
Member
Registered: 2013-02-07
Posts: 3

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

Offline

#12 2013-02-10 23:23:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,716

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

Board footer

Powered by FluxBB