# Rope Around The Earth

 It was an interesting question as to how to define a metre. One of the original ideas was that it should be the length of a pendulum such that a half-swing would take one second. Seemed to be about right - a good length to use. Problem it, that depends on where you are - higher altitude means lower value of local gravity, so you need a shorter pendulum. So in the end they defined - by fiat - that it would be 10 million metres from the North Pole to the Equator on the longitude that passes through Paris. Hence the Earth's circumference is 40 million metres.
A chap manages to find on the internet the kind of rope you only ever find in physics and maths problems. It's light, inextensible, and as long you you want.

Knowing that the Earth is 40 million metres in circumference (because that's how the metre was originally defined) he buys 40 million metres of rope, and sets off to girdle the Earth.

When he returned back to his start point he found that he had 6 metres of rope left over! So he sets off to prop up the rope, distributing the excess equally around the world. All around he lifts the rope a little off the surface, and in doing so he takes up the slack.

Assuming it's the same height everywhere, how high is the rope off the surface?

• An atom's width?
• The thickness of a sheet of paper?
• A finger's width?
• Can you crawl under it?
• Can you walk under it?
• Is it the height of a building?
Many people simply don't believe the answer - it's about 95 cm high, all the way around. Being comfortable with algebra the answer is easy - circumference is 2.pi.R, so an increase of 1 in the radius increases the circumference by 2.pi, which is a little more than 6. To get an increase of exactly 6 then requires an increase of just a little less than 1, 6/(2.pi) to be exact.

Which is 95 cm.

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