Please help: How do you find the peremeter of an oval

[Register]

Please give me the formula.

Your help is appreciated.
Thanx in advanced.

 

[arildno]

Are you thinking of the perimeter of an ellipse?

As it happens, the formula is some nasty infinite series, if I'm not mistaken.

 

[Register]

Sorry, I don't know what an ellipse is. I mean an oval with a radius of 20CM horizontally, and 7CM vertically.

I know that the formula to find it's area is:
20 X 7 X 3.14

I know there is a way to find it's perimeter. :p

 

[dextercioby]

Sorry, I don't know what an ellipse is. I mean an oval with a radius of 20CM horizontally, and 7CM vertically.

I know that the formula to find it's area is:
20 X 7 X 3.14

I know there is a way to find it's perimeter. :p

It is.It is called COMPLETE ELLIPTIC INTEGRAL OF THE FIRST KIND OF ANDRE MARIE LEGENDRE.
Do you want the formula,the series exapansion??

Daniel.

 

[Register]

Yes, please give me the formula. ^_^

 

[dextercioby]

There you go,for an ellipse of semiaxis "a" and "b" it reads
$$I_{ellipse}(a,b)=:4\int_{0}^{+\frac{\pi}{2}} \sqrt{a^{2}\sin^{2}\phi+b^{2}\cos^{2}\phi} d\phi$$

Daniel.

 

[Register]

Thank you so much. You really helped a lot. ^_^

 

[dextercioby]

Thank you so much. You really helped a lot. ^_^

You're welcome... I just hope u know you can't solve that integral exactly,doncha??I'm hoping you won't be spending your whole day trying to find the antiderivative and applying the Leibniz-Newton formula...
This integral is tabulated in many engineering books...


Daniel.

 

[Alex]

Thank you so much. You really helped a lot. ^_^

Not to be rude, but, I find it that hard to believe considering that you didn't know what an ellipse was.

 

[rachmaninoff]

Just wondering, is an oval actually an ellipse at all? Since an oval is the shape of an egg, and an egg only has one axis of symmetry (I mean a chicken egg). It's longer on one end, and rounder on the other.

 

[master_coda]

Just wondering, is an oval actually an ellipse at all? Since an oval is the shape of an egg, and an egg only has one axis of symmetry (I mean a chicken egg). It's longer on one end, and rounder on the other.

You're right, an oval isn't an ellipse. I've never actually seen a precise mathematical definition of an oval (i.e. I don't know what the general equation of an oval is) but it would certainly not be the same as that of an ellipse.

However in this case I suspect that Register is actually talking about an ellipse and just doesn't know the correct name for it. The area equation given as an example is after all the equation for the area of an ellipse.

 

[BobG]

You might want an approximation.

Try this (scroll down to equation 66) for a reasonable approximation:
http://mathworld.wolfram.com/Ellipse.html

Or this for a couple of other versions:
http://www.mechanicaldesigner.com/Ellipse.html