Math Question

[Marcie]

Is there an equation for the circumference of an ellipse? If so, what is it?

I ask this 'casue I remember my math program a couple years ago stating that there wasn't one.

[Kings]

I don't think there is one..

[Patchy]

Moved to education and careers.

[Malcolm Tucker]

Sorry but there is no way to find it for definite. However there is ways to approximate it. I don't know the series or formula for that but I'm sure if you ask your teacher you'll find out.

[Magus]

There is a chapter called conics section, set for things like Parabola and Ellipse, but that's for dimensional values and not metrical values.

I don't know if there is one I passed by.

[Katrina]

The circumference C of an ellipse is http://upload.wikimedia.org/math/b/0/1/b01de9a2a82e22c2aba611cdc7f93285.png, where the function E is the complete elliptic integral of the second kind.

[Marcie]

The circumference C of an ellipse is http://upload.wikimedia.org/math/b/0/1/b01de9a2a82e22c2aba611cdc7f93285.png, where the function E is the complete elliptic integral of the second kind.

Okay, thanks :-)

And thanks to everybody else for their input.

Though I have one more question.
Wouldn't it make sense to have the circumference of an ellipse as the average of the long and short diameter times Pi? Because by taking the average wouldn't that, in effect, mold it to a circle while retaining the came circumference?
Just a thought.

[INFERNO]

Okay, thanks :-)

And thanks to everybody else for their input.

Though I have one more question.
Wouldn't it make sense to have the circumference of an ellipse as the average of the long and short diameter times Pi? Because by taking the average wouldn't that, in effect, mold it to a circle while retaining the came circumference?
Just a thought.

Taking the average of the long and short diameters would be very unlikely to make it equal to that of a circle. Depending on the numbers, it may but more often than not, it's not going to. Try it for yourself, let's say the circle diameters is 5 cm, the long diameter of the ellipse is 10 cm and the short is 3 cm. The average is 6.5 cm, so although it's close it's not the same. The reason is in an ellipse, the radius is constantly changing whereas in a circle, it's always the same, so the average of just the 2 diameters of an ellipse doesn't capture this defining feature. In other words, it involves calculus because the radius is always changing, so although the average may be close to that of the circle, it won't be equal in most cases.

[Marcie]

Taking the average of the long and short diameters would be very unlikely to make it equal to that of a circle. Depending on the numbers, it may but more often than not, it's not going to. Try it for yourself, let's say the circle diameters is 5 cm, the long diameter of the ellipse is 10 cm and the short is 3 cm. The average is 6.5 cm, so although it's close it's not the same. The reason is in an ellipse, the radius is constantly changing whereas in a circle, it's always the same, so the average of just the 2 diameters of an ellipse doesn't capture this defining feature.

In your example, are the circumferences of the two shapes the same? because otherwise that example doesn't really hold water..

[INFERNO]

In your example, are the circumferences of the two shapes the same? because otherwise that example doesn't really hold water..

You were asking about whether the average of the long and short diameters of an ellipse will "mold" an ellipse to that of a circle to get the circumference, so really, you're asking whether C = (pi)d of a circle can become 4aE(e^2), where E is an integral for the ellipse. This has nothing to do with knowing whether the circumferences are equal, it comes down to pure math because you'd need for C = (pi)d to somehow satisfy a changing radius, which it does not do. The example was simply meant to illustrate this point.

Suppose that the circumference of the circle and ellipse were equal, for certain values of the radii, which is what you're proposing now. What does that show? It only has any value if the equations for the two shapes can produce equal results, that is, if one equation can be derived into another. Hence, I return to why I addressed the equations to begin with, in the above paragraph.