A2-61.HTML
A2-61: EXPONENTIAL INCREASE - CHESSBOARD AND RICE

PURPOSE: To illustrate exponential increase from 1 through 2**64.

DESCRIPTION: The transparent chessboard serves as the starting point for the progression. Rice can be put on the chessboard for 1 through 2**5 (32) grains. Use beakers for 2**6 through 2**17 grains. (Note: 1 ml = 64 grains, approximately.) The approximate volume of rice for successive powers of two are:

2**18 - 2**20: small waste basket, to 5.6, 11, and 22 cm, respectively.
2**21 - 2**22: large waste basket to 31 and 62 cm, respectively.
2**23 - 2**27: area of 1mx2m lecture table to 6.5, 13, 25, 50, and 100 cm, respectively.
2**28 - 2**37: area of front of room to 1, 2, 4, .......512 cm, respectively.

The total amount of rice is 2**65 - 1, or 3.7x10**19 grains. This is approximately four crops at 100 bushels per acre, with the entire land area of earth (about 4x10**11 acres) planted with rice!

SUGGESTIONS: Tell them the story about the invention of chess.

REFERENCES: (PIRA unavailable.)

EQUIPMENT: Rice, labeled containers through 2**16, transparent chess board.

SETUP TIME: 5 min.