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Prove this wrong! - HSN forum

# Prove this wrong!

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### #1Floorball Maniac

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Posted 21 June 2006 - 09:45 PM

http://plus.maths.org/issue39/puzzle/index.html

### #2Changer

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Posted 22 June 2006 - 12:27 AM

That bottom equation doesn't look right

As n tends to inf, 0.5^n will tend towards 0...right?
I'm not sure it's 01:27 in the morning

### #3George

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Posted 22 June 2006 - 03:37 PM

I think I know what the problem is, but I don't want to give it away

### #4Changer

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Posted 22 June 2006 - 07:53 PM

Is it something...painfully...obvious?

### #5George

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Posted 22 June 2006 - 10:55 PM

I spotted a problem reading through it the first time, but only because I've seen something similar recently

If I'm right, it's not really an obvious mistake.

### #6Changer

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Posted 22 June 2006 - 11:07 PM

Will you either reveal or PM me your thoughts?

### #7waitingforan_alibi

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Posted 29 June 2006 - 07:42 PM

i think the answer is in the line "The string of semi-circles approximates the diameter d". When you half the diameter of the semicircle the circumference of the semicircle halfs, but there are two semicircles so the total length is the same as the original even if you half it infinte times. my point is that if you keep halving the diameter of the semi circles a picture of it would look like a straight line (if you half it enough times) but it is pi times longer than the straight line it looks like - thats where the mistake is

### #8George

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Posted 29 June 2006 - 08:55 PM

I agree

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