Imagine, if you will, a very long piece of ropethat loops around the Earth, fitting it tightly around the equator like a belt. If you wanted to raise this rope off the surface by one metre all around, how much more rope will you need?
The length of rope is the same as the circumference of the Earth which is 40,075km (24,901 miles). Ergo, it is easy to think that you would need kilometres of rope to extend it enough to float a metre off the Earth’s surface. However, in reality you need a mere 6.28m of extra rope to achieve this.
The reason is extremely simple, mathematically speaking. The circumference of any given circle is given by the equation 2πr, where r is the radius of the circle. Therefore, if you increase r by 1 unit (e.g. 1m), then the circumference increases by 2π x 1 = 2π = 6.28. No matter how large the circle may be, this rule does not change.
(This is a famous maths riddle, but here’s a much more interesting application of the concept in this What If? article. God I love that blog! http://what-if.xkcd.com/67/)
