
Ellipse Geometry
Hi All
Can anyone help me with regards ellipse geometry. (Headbang)
I have an issue were i have to be able to calculate the major and minor axis of an ellipse when i have the circumference.
I know Ellipse Circumference = pi*sqrt((major^2+minor^2)/2)
My relation from major to minor is: major = minor + constant (say 2.5 to start)
This now leaves me with:
Ellipse Circumference = pi*sqrt(((minor + 2.5)^2+minor^2)/2)
I have rearranged the equation to give me:
2*((ellipse circumference/pi)^2) = (minor + 2.5)^2 + minor^2
Continuing to manipulate I get:
2*((ellipse circumference/pi)^2) = 2*minor^2 + 5*minor + 6.25
I am now stuck on where to go to calculate minor if i know the circumference as using a quadratic equation b (+/) sqrt(b^24ac)/2a I am left with a negative square root which i can not solve.
Can anyone HELP, where do i go from here?

I may be misunderstanding, but the length of an ellipse circumference is not
gotten by that formula. As a matter of fact, the circumference of an ellipse is
rather difficult to calculate. That is where Elliptic integrals come in.

Ellipse Geometry
Hi Galactus
I got the approximation formula from the following link
www.csgnetwork.com/circumellipse.html
Ive done an initial bit of rearranging which i why my formula stated looks different to that in the link.

For a closed ellipse , the length of the ellipse circumference is
$\displaystyle 2a\pi [ \sum_{n=0}^{\infty} (\frac{k}{16})^{n} \frac{ [\binom{2n}{n}]^2}{12n} ]$
with major a and minor b (a>b) , $\displaystyle k = \frac{a^2  b^2}{a^2}$

simplependulum
Given that formula you have can you tell were it came from?,
Given that formula you have stated, what is "n", and how would i solve to get a or b, i will still be left with having to solve 2*minor^2 + 5*minor + 6.25 were i replace a with b + constant (2.5)
Cheers