🌍 A rope around the Earth is 1 meter longer - and a cat can crawl under it.
This is a well-known problem, but it always boggles the mind. Imagine the Earth as a perfect sphere with a perfectly circular equator, and we tie a rope exactly the length of the equator. We add just 1 meter to this rope and make it a circle again - a hoop with a slightly larger radius. The question is: what gap will be created between the Earth's surface and this hoop?
Intuition suggests that the gap will be microscopic - a meter against a circumference of 40,000 km is nothing. The gap turns out to be almost 16 cm, and a cat can easily crawl through.
It's calculated in one line. The circumference grows as 2πr, so the difference in lengths 2π(R-r) = 100 cm gives R-r = 100/2π ≈ 15.9 cm - and this number does not depend on the initial radius r. Whether it's the Earth, the Universe, a basketball, or a pea - an extra meter of rope always gives the same gap.
#math@rvnikita_blog #interesting@rvnikita_blog #fact@rvnikita_blog
