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.

Possible Duplicates:
Why is Euclidean geometry scale-invariant?

Proof that Pi is constant (the same for all circles), without using limits

The answer with the most up votes will be selected as the answers after 72-hours has passed.

Questions, feedback, requests -- just comment, thanks!!

share|improve this question

marked as duplicate by Ross Millikan, Chandru1, Qiaochu Yuan Feb 26 '11 at 19:38

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

3  
Did you mean why is the ratio of circumference of a circle to diamter independent of the circle? –  Aryabhata Feb 26 '11 at 19:08
1  
What definition of $\pi$ are you using that might make it not a constant? What would cause it to vary? Vote to close as not a real question. –  Ross Millikan Feb 26 '11 at 19:09
1  
I think the new version of the question is a good one. –  Mike Spivey Feb 26 '11 at 19:28
1  
Duplicate: math.stackexchange.com/questions/23129/… –  Qiaochu Yuan Feb 26 '11 at 19:38
3  
@blunders: Take a look at this also: math.stackexchange.com/questions/3198/… –  Derek Jennings Feb 26 '11 at 19:47

1 Answer 1

up vote 1 down vote accepted

Because when you change the scale, both the diameter and the circumference change by multiplying by the same scale factor, since they are both of dimension 1. Thus, their ratio is independent of the scale factor. Since all circles are similar, the ratio is the same for all circles.

share|improve this answer
    
+1 Funny thing is, your answer makes sense to me -- the answer and question linked to as a duplicate... does not - oh, well. –  blunders Feb 26 '11 at 19:50
1  
@blunders: You may appreciate these answers (added again here as the identical link is a bit lost in the comments to the question): math.stackexchange.com/questions/3198/… –  Derek Jennings Feb 26 '11 at 19:59
    
@Derek Jennings: +1 Thanks! –  blunders Feb 26 '11 at 20:09

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