Difference between revisions of "CSC103: DT's Notes 1"
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[[Image:LilyInPond.png|200px|right]] | [[Image:LilyInPond.png|200px|right]] | ||
| − | ::''Suppose a lily is in the middle of a | + | ::''Suppose a lily is in the middle of a pond, and every day it doubles in size. In 30 days the lily has covered half of the pond. How long will it take it to cover the whole pond?'' |
| − | If you answered 31 days, then congratulations! Indeed, if it doubles in size every day, then after Day 30 it will be twice half the size of the | + | If you answered 31 days, then congratulations! Indeed, if it doubles in size every day, then after Day 30 it will be twice half the size of the pond, so it will have covered the whole pond! This simple example shows the powerful nature of exponential growth. It took the lily 30 days to cover 50% of the lake, but it takes in only 1 day to cover the other 50%. |
| − | There are many such puzzles in our cultures that attempt to demonstrate the extraordinary power of exponential growth through seemingly impossible feats. Another is the story rice on | + | There are many such puzzles in our cultures that attempt to demonstrate the extraordinary power of exponential growth through seemingly impossible feats. Another one is the story of grains of rice on a chessboard as told by David R. Henderson and Charles L. Hooper<ref name="rice">David R. Henderson and Charles L. Hooper, ''Making Great Decisions in Business and Life'', Chicago Park Press, 1st edition, March 12, 2007.</ref>: |
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:::In a time of hunger, the Emperor of China wanted to repay a peasant who had saved the life of his child. The peasant could have any reward he chose, but the Emperor laughed when he heard the silly payment the foolish peasant selected: rice on a chessboard. The peasant wanted one grain of rice on the first square, doubling to two on the second, doubling to four on the third, and so on. After the Emperor agreed, his servants brought one bag of rice into his court and began tediously counting rice. Soon, he called for more and more bags of rice... | :::In a time of hunger, the Emperor of China wanted to repay a peasant who had saved the life of his child. The peasant could have any reward he chose, but the Emperor laughed when he heard the silly payment the foolish peasant selected: rice on a chessboard. The peasant wanted one grain of rice on the first square, doubling to two on the second, doubling to four on the third, and so on. After the Emperor agreed, his servants brought one bag of rice into his court and began tediously counting rice. Soon, he called for more and more bags of rice... | ||
Revision as of 07:29, 1 October 2013
--© D. Thiebaut 08:10, 30 January 2012 (EST)
