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Old 1st October 2012, 02:54 PM   #131
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Consider the earth to be spherical with a circumference of 40,000 kms. A string, wrapped around the earth, would measure 40,000 kms. Take another string and raise it 1 cm from the first and go around the earth again. How much longer is the second string?
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Old 1st October 2012, 04:48 PM   #132
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2πcm
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Old 3rd October 2012, 07:56 AM   #133
terry j is offline terry j  Australia
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Quote:
Originally Posted by Cal Weldon View Post
Consider the earth to be spherical with a circumference of 40,000 kms. A string, wrapped around the earth, would measure 40,000 kms. Take another string and raise it 1 cm from the first and go around the earth again. How much longer is the second string?
Radius of earth is Re. Length of string is 2piRe (or whatever!)

Radius of raised string is (Re + 1cm)

length of that string is 2piRe + 2picm

therefore difference in strings is (2piRe + 2pi cm - 2pi Re)=2pi cm.

Good question, very counterintuitive.


(check my maths tho haha, the reasoning is correct)

Oops, plastic got it first, just realised what looks like an n to me without glasses is prob pi.
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Old 3rd October 2012, 02:15 PM   #134
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Oops, plastic got it first, just realised what looks like an n to me without glasses is prob pi.
It took so long to find on this Windows 7 machine. I was mortified to find the top bar has lost its wiggle. What happened to extended ascii?

It's quite an instructive problem. The relationship between radius and circumference is linear, so simple superposition applies. Counterintuitive perhaps because our conception of the size of a circle is more related to area than to radius or circumference.
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Old 3rd October 2012, 04:24 PM   #135
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I think because it's 40,000km, the initial reaction is: It has to be way longer, now let's go find out how much. Hmmm...
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Old 3rd October 2012, 04:26 PM   #136
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Old 3rd October 2012, 04:48 PM   #137
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What occurs once in a minute, twice in a moment, but never in a thousand years?
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Old 3rd October 2012, 05:31 PM   #138
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"m"
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Old 3rd October 2012, 06:16 PM   #139
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Old 3rd October 2012, 06:16 PM   #140
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Accessories/system tools/character map.

π

That's Palatino. This editor ignores the typeface of imported text, so I changed the font after pasting.
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