Suppose you wrap a (fairly long) rope tightly around the earth’s equator. Now you insert one meter of additional rope and you evenly lift the rope of the earth’s surface. By how much (roughly) will it lift of the ground? 1 micrometer? 1 millimeter? 1 decimeter? 1 meter?

Most people will guess something between a micrometer and a millimeter. Others will first ask for the circumference of the earth (about 40,000 km). But the answer is quite counter-intuitive.

If you ask people directly what the relation between the radius and the circumference of a circle is many will know that U=2*pi*r, or alternatively r=U/(2*pi). But not so many will have the immediate (trivial) intuition that this means that if you increase the circumference by x, the radius will increase by x/(2*pi), regardless of the radius or the circumference. So the rope will be lifted off the ground by roughly 16 cm (~ 1m/(2*pi)), which is also the radius of a circle you’d get by simply taking the one meter of rope and making a nice symmetric loop out of it.

I still find this very strange, even though it’s completely trivial.