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.

]]>Try calculating the values of

using Wolfram Alpha (link).]]>

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

]]>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...

]]>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.

]]>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...?)

]]>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.

]]>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

]]>Thank you all in advance for your time.

]]>