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Elipse perimeter

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abilicious | 14:19 Fri 18th Aug 2006 | Science
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My 11 year old has suggested that to find the perimeter of an elipse you should measure the shortest distance across the elipse and the longest distance, multiply them together and divide the answer by two, then multiply by pi. Is this right? (Over my head, I'm afraid).

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What your daughter is thinking is this: you need to do Measure the shortest and longest sides, then ADD them together, divide the answer by two, and then multiply that answer by Pi. The area of a CIRCLE is Pi x Diameter of circle. All that the above method does is averages the diameters to effectively create a circle. Which to be honest is good maths for an 11 year old, but is incorrect. As rojash posted in his link, it is seriously complicated, but here is an elliptical calculator to work our the circumference. http://www.csgnetwork.com/circumellipse.html so just insert the values that your daughter suggested you measured in the first place.
The area of an ellipse is pi.a.b where a and b semi major and semi minor axes - any A level student should be able to prove that.

The circumference is a different matter. You have to sum all the little steps as you go around the ellipse. And you get a equation which is called an elliptical integral. and then you read a book written by mathematicians on these things, because they cant be solved. That is, you cant get a formula like pi.a.b or 2 pi.r
butbut but, you can do approximations and the URL above takes you to quite a good site.

Go on envouraging your child - you do quite a lot about ellipses at A level.

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