Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can you produce an example where both the area of a circle and it's radius are integers?

share|improve this question
5  
No, if that were true then $r^2$ would be an integer and then $\pi=\frac{A}{r^2}$ would be rational, which it isn't. –  Tom Oldfield May 18 '13 at 18:34
    
If r = 0 because then A = 0. But that's hardly an example, is it? Otherwise Tom answered it. –  imranfat May 18 '13 at 18:36
2  
@Tom: That's an answer, not a comment. –  Asaf Karagila May 18 '13 at 18:54
    
@Asaf I suppose, I wrote it up as one at first but I didn't feel like I had put enough work into it to make it an answer! I was sure that someone else would point out the exact same thing (and I hate it when some questions receive many almost identical answers). If no-one did I would have changed it into an answer at some point for completeness. –  Tom Oldfield May 18 '13 at 21:00
    
there is $1019514486099146/324521540032945$ or $20,000,000/2325^2$ but it isn't pi. –  user52413 Aug 23 '13 at 13:07
add comment

1 Answer 1

up vote 3 down vote accepted

$$r\neq 0\;,\;\pi r^2\;,\;r\in\Bbb N\implies \pi\in\Bbb Q\;,\;\text{which is false}$$

share|improve this answer
    
OK, then is it correct to say that at least one among A and r has to be irrational. –  BlueFlame May 18 '13 at 18:54
    
Yes, it is correct. –  DonAntonio May 18 '13 at 18:56
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.