lasy joe is sitting on a beach chair, somewhere in Sudan, sipping a martini. The piece of string which surrounds the earth (which happens to be a perfect sphere) lay on the earth beside him. So joe decided to play a joke on the rest of the world so he cut the string, added a 1meter piece of string to it and then went around the world, raising the string up from the ground so that it is evenly spread around the globe again only off the ground. When he gets home, he sees his two legged cat bipod crying because his milk dish is on the other side of the string and now that it's off the ground, bipod can't get passed it.....

here's the question: (finally) is the piece of string high enough off the ground for an average sized bipedded cat can get under it..

Originally posted by Asher123 lasy joe is sitting on a beach chair, somewhere in Sudan, sipping a martini. The piece of string which surrounds the earth (which happens to be a perfect sphere) lay on the earth beside him. So joe decided to play a joke on the rest of the world so he cut the string, added a 1meter piece of string to it and then went around the world, raising the string up ...[text shortened]... nd for an average sized bipedded cat can get under it..

the answer shocked the hell out of me

circumference = 2*Pi*R

so set 2*Pi*R_old + 1 meter = 2*Pi*R_new

then the new radius is the old radius plus 1/(2*Pi) meters.
so the string should be about 6 inches off the ground in the final state.

i think a cat could probably squeeze under that. It is a surprising result that the string is now that high off the ground.

Originally posted by davegage circumference = 2*Pi*R

so set 2*Pi*R_old + 1 meter = 2*Pi*R_new

then the new radius is the old radius plus 1/(2*Pi) meters.
so the string should be about 6 inches off the ground in the final state.

i think a cat could probably squeeze under that. It is a surprising result that the string is now that high off the ground.

correct!
2PiR=circumference (C)
which means R=C/2Pi
new R=New C/2Pi
=> new R =(C+1)/2Pi
=> new R = C/2Pi + 1/2Pi
c/2pi has already been established as R
=> new R= R + 1/2Pi meters

so yup that's aboot 6 inches more or less. Isn't that odd?

Certainly seems weird. If you have zero start circumference, or the size of the universe - the increase in radius when you add 1 metre to the circumference is the same.

exactly - 2PiR shows us more than a simple ratio it shows that the increase in circumference affects the radius at 1:1/2Pi regardless of the actual values