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A2-61: EXPONENTIAL INCREASE - CHESSBOARD AND RICE 9 years 10 months ago #224

  • mike1
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ID Code: A2-61
Purpose: Illustrate exponential increase from 1 through 2^63
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 2^63 - 1, or about 9.2x10^18 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.

Availability: Available

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