My Math Forum Circumference of an Ellipse

 Calculus Calculus Math Forum

 June 25th, 2017, 02:37 PM #1 Newbie   Joined: Jun 2017 From: Tennessee Posts: 1 Thanks: 0 Circumference of an Ellipse Approximate, within an error of 0.001 units, the circumference of the ellipse given by the equation (x/3)^2+(y/2)^2=1
 June 25th, 2017, 03:19 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,737 Thanks: 1387 $x = 3\cos{t}$ $y = 2\sin{t}$ $\displaystyle C = 4\int_0^{\pi/2} \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt} \right)^2} \, dt$ $\displaystyle C = 4 \int_0^{\pi/2} \sqrt{9\sin^2{t}+4\cos^2{t}} \, dt \approx 15.865$ Thanks from Country Boy
 July 1st, 2017, 10:07 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,109 Thanks: 855 The reason the problem asks you to "Approximate, within an error of 0.001 units" is that we cannot do this integral "analytically". It is one of a class of integrals called "elliptic integrals". I remember, many, many years ago seeing. in a University library, an entire shelf of, I think, 20 large volumes giving numerical values of the elliptic integrals. You will need to complete this problem using some numerical integration method. Thanks from 123qwerty
July 1st, 2017, 10:17 AM   #4
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Quote:
 Originally Posted by Country Boy The reason the problem asks you to "Approximate, within an error of 0.001 units" is that we cannot do this integral "analytically". It is one of a class of integrals called "elliptic integrals". I remember, many, many years ago seeing. in a University library, an entire shelf of, I think, 20 large volumes giving numerical values of the elliptic integrals. You will need to complete this problem using some numerical integration method.
20 large volumes! How times have changed with the advent of computers...

July 1st, 2017, 04:45 PM   #5
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Quote:
 Originally Posted by 123qwerty 20 large volumes! How times have changed with the advent of computers...
This was in 1970 and the numbers in those volumes had been calculated by computer. But it was much easier to carry the relevant volume around with you than to carry a computer!

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