The power of one

"IT may be the loneliest digit in the world, but not underestimate the power of one," says Zeus to Hercules before he is to begin his next adventure. "Son, I would also like you to remember that whatever is on top always returns to bottom," says Zeus. "I shall remember that, father," says Hercules. He is to report to Atlas at the top of Mount Olympus to receive the first of his 12 tasks.

"I was expecting you to be here," says Atlas on receiving Hercules, "prepare for a long journey because we are going around the world." Atlas is carrying a huge net roll on his shoulder, which he unrolls with every step. "See that the net is tied tightly to every bit of the ground that we cover," he says to Hercules. They cross gorges, plains, deserts, forests, mountains and oceans, covering the equator to finally reach Mount Olympus again. The net is hugging the ground firmly all along the way.

"Is my task over?" says Hercules. "It has just begun dear," says Atlas, "You have tied the net so tightly around the Earth that a leaf cannot be squeezed underneath it. You have to make space for millions of my rabbits around the world to squeeze underneath this net and you have to do it without leaving Mount Olympus.

If you fail to do it, I shall kill you." Hercules realises that he is trapped and remembers what his father had told him before the journey — "Do not underestimate the power of one." He cuts the net from a point and adds an extra metre to it. "Your rabbits are welcome to cross over to the other side," says Hercules. "Impossible," says Atlas, "Compared to the enormous length of the net around the Earth, you have added only one metre to it. If millions of people spread out all along the net try to lift it up at the same time now, I am sure that they will not be able to get even their fingers underneath it."

Hercules says, "To prove that what I say is true, I will have to use some simple algebra. If the diameter of Earth is D, its circumference C is equal to pi×D, which is also the circumference of the net. When we add a metre to the net, the new circumference Cnew is equal to pi×(D + S), where S is the extra diameter of the net. However, we know that Cnew is equal to C + 1, so pi×D + 1 = pi×D + pi×S. We cancel out the pi×D to get 1 = pi×S, or S = 1/pi, which is roughly 32 cm. If the extra diameter is about 32 cm, it means that the extra radius is 16 cm. This means that the circle of net will now clear Earth by 16 cm all the way around the equator, which is more than enough space for all of your rabbits to crawl through."

Atlas says, "You have accomplished this task, but how will you face all by yourself the other challenges that your stepmother Hera has chosen for you?" "Never underestimate the power of one," says Hercules and climbs down the mountain. Zeus had said, "What goes up, comes down."

— Aditya Rishi