# Ellipse Geometry

• July 10th 2009, 07:51 AM
Matty B
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 re-arranged 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^2-4ac)/2a I am left with a negative square root which i can not solve.

Can anyone HELP, where do i go from here?
• July 10th 2009, 08:29 AM
galactus
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.
• July 10th 2009, 10:11 AM
Matty B
Ellipse Geometry
Hi Galactus

I got the approximation formula from the following link

www.csgnetwork.com/circumellipse.html

Ive done an initial bit of re-arranging which i why my formula stated looks different to that in the link.
• July 11th 2009, 01:46 AM
simplependulum
For a closed ellipse , the length of the ellipse circumference is

$2a\pi [ \sum_{n=0}^{\infty} (\frac{k}{16})^{n} \frac{ [\binom{2n}{n}]^2}{1-2n} ]$

with major a and minor b (a>b) , $k = \frac{a^2 - b^2}{a^2}$
• July 12th 2009, 12:21 AM
Matty B
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