Spot the error! (circumference of ellipse)

  • #1
1,434
2
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.)
 

Answers and Replies

  • #2
52
0
I could not see the mistake yet.. Interesting way to calculate the circumference :)
 
  • #3
22,089
3,286
(I couldn't post this in the Math forum since they would just yell at me for using the dirac delta
Well, I just moved it to the math forum. So prepare for some yelling :biggrin:
 

Related Threads on Spot the error! (circumference of ellipse)

  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
9K
Replies
7
Views
3K
  • Last Post
Replies
12
Views
7K
  • Last Post
Replies
6
Views
13K
  • Last Post
Replies
3
Views
586
  • Last Post
Replies
3
Views
1K
Replies
3
Views
6K
  • Last Post
Replies
3
Views
2K
Replies
1
Views
2K
Top