1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spot the error! (circumference of ellipse)

  1. Jan 10, 2012 #1
    Spot the error:

    The circumference of an ellipse with semi-major axis = 2 and semi-minor axis = 1 (i.e. [itex] \left( \frac{x}{2} \right)^2 + y^2 = 1 [/itex]) is [itex]4 \pi[/itex]. Proof:

    [itex]\textrm{circumference} = \iint_{\mathbb R^2}{ \delta \left( \left( \frac{x}{2} \right)^2 + y^2 - 1 \right) } \mathrm d x \mathrm d y = 2 \iint_{\mathbb R^2}{ \delta \left( \left( \frac{x}{2} \right)^2 + y^2 - 1 \right) } \mathrm d \frac{x}{2} \mathrm d y = 2 \iint_{\mathbb R^2}{ \delta \left( x^2 + y^2 - 1 \right) } \mathrm d x \mathrm d y = 2 \times 2 \pi = 4 \pi [/itex]

    (I couldn't post this in the Math forum since they would just yell at me for using the dirac delta, and it's also not homework as I know the answer.)
  2. jcsd
  3. Jan 10, 2012 #2
    I could not see the mistake yet.. Interesting way to calculate the circumference :)
  4. Jan 10, 2012 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Well, I just moved it to the math forum. So prepare for some yelling :biggrin:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Spot the error! (circumference of ellipse)
  1. Circumference of a Ball (Replies: 12)