Kinesys settles on Polygon beside a monument shaped like an icosahedron. A local guide is telling tourists about the oddities of other planets. “On Earth,” he announces with a shudder, “the planet is almost perfectly spherical!” The audience shudders too.
Liz, who happens to come from Earth, feels obliged to defend it. So the guide challenges her with an ancient Earth puzzle, much loved on Polygon because it shows just how deceptive curves can be.
Dord listens with an air of superiority: he has never understood curves and has no intention of starting now. M00N, on the other hand, is thrilled: the puzzle has animals in it, and she adores all of them.
The Riddle
Imagine a rope as long as Earth’s circumference (about 25,000 miles), laid along the equator. Now imagine cutting the rope, adding one yard (3 feet) to it, and spreading it back around the equator so that its distance from the ground stays the same all the way around.
Which of these three animals could fit through the gap between the rope and the ground: an ant, a cat, or an elephant?
Hint
You don’t need Earth’s radius. Write the circumference before and after adding the extra yard, and see how much the radius changes.
Solution
The answer is: a cat.
The answer is surprising, because we tend to assume that lengthening such an enormous circle by such a tiny fraction must raise the radius by an equally tiny amount. Not so: the increase in the radius depends only on the length of rope added, not on the radius of the original circle.
If R is Earth’s radius and C = 2πR its circumference, both in inches, and the added yard is 36 inches, the distance between the rope and the ground is:
d = (C + 36) / (2π) − R = 36 / (2π) ≈ 5.7 inches
That’s just under 6 inches: plenty for an ant, enough for a cat (which is always happy to squeeze through), and far too little for an elephant.