Logic puzzles

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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?

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.
 
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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