The Chessboard and Exponential Growth

64 = 8² = 2⁶. The legend: place one grain of wheat on the first square of a chessboard, two on the second, four on the third, doubling each time. The total — 2⁶⁴ − 1 — is approximately 18.4 quintillion grains, enough to cover all of India one metre deep. The king who agreed to this payment could not possibly honour it. This story, told for over a thousand years, is the canonical illustration of exponential growth: numbers that seem manageable for 32 steps become incomprehensible by step 64.