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1st October 2012, 02:54 PM  #131 
Speakerholic
diyAudio Moderator

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?

1st October 2012, 04:48 PM  #132 
diyAudio Member
Join Date: Mar 2012
Location: Bradford

2πcm

3rd October 2012, 07:56 AM  #133  
diyAudio Member
Join Date: Aug 2006

Quote:
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. 

3rd October 2012, 02:15 PM  #134  
diyAudio Member
Join Date: Mar 2012
Location: Bradford

Quote:
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. 

3rd October 2012, 04:24 PM  #135 
Speakerholic
diyAudio Moderator

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...

3rd October 2012, 04:26 PM  #136 
Speakerholic
diyAudio Moderator


3rd October 2012, 04:48 PM  #137 
Speakerholic
diyAudio Moderator

What occurs once in a minute, twice in a moment, but never in a thousand years?

3rd October 2012, 05:31 PM  #138 
diyAudio Member

"m"
__________________
The Devil is not so terrible as his math model is! 
3rd October 2012, 06:16 PM  #139 
Speakerholic
diyAudio Moderator


3rd October 2012, 06:16 PM  #140  
diyAudio Member
Join Date: Mar 2012
Location: Bradford

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

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