Monday, December 18, 2006

How much rope?

A fool wants to tie a rope around the earth. So he buys a rope of 40,000 KM and ties it around the world. His neighbor, also a fool, wants to do the same only he wants the rope on sticks 1 meter above the ground.

How much more rope does he need?
And how much more rope do you need when you use a tennis ball instead of the earth?

1. the answer would seem to be 2*pi meters in both cases. since rope length is circumference, which is 2*pi*radius, and in both cases you are increasing the radius by 1 meter.

2. It does seem counter-intuitive, doesn't it? But yes, Andy is correct. For both instances, you add just over 6 meters of rope and you have extended the radius by 1 meter. How cool is that?

3. It's very cool.

The outline of a circle is 2*PI*r. If you want a rope that is one meter above the ground rnew=r+1. So you need 2*PI*(r+1)-2*PI*r more rope.

So,
x=2*PI*(r+1)-2*PI*r
x=2*PI*r+2*PI-2*PI*r
x=2*PI
x is approximately 6.28 meters

It does not matter what the radius of the circle is. You always need 2*pi more rope.

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