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To answer that we would have to take a look at how the formula is derived.
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
using Wolfram Alpha (link).
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
It's too bad that there is no exact closed formula for the ellipse circumference...
Thanks for confirmation! I just entered some random values for a and b in for WolframAlpha and it came up with that too...
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.
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:
As for the calculation of the perimeter of an ellipse... well, my first thought was just to say
General form of an ellipse:
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...?)
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.