Difference between revisions of "CSC103: DT's Notes 1"
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<center>[[Image:CSC103_ExponentialGrowth1.png|450px]]</center> | <center>[[Image:CSC103_ExponentialGrowth1.png|450px]]</center> | ||
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| − | Note the quick growth of the | + | Note the quick growth of the points in the graph. To get the full impact of the exponential growth we need to plot a few more points, first from Square 1 to 13, then from Square 1 to 25, and finally from Square 1 all the way to 64, as illustrated in the plots below: |
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| − | What is important to see here is that as we show more and more squares, the actual growth that takes place for squares of low order | + | What is important to see here is that as we show more and more squares, the actual growth that takes place for squares of low order, say, less than 40, is completely obfuscated by the large size of the quantities associated with the squares of higher order, |
| + | even though the number of grains on the 40th square is an impressive 549,755,813,888! | ||
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| + | The last plot in the series, where all the squares from 1 to 64 are shown actually flattens everything except for Squares 55 and up. It also shows why people have referred to exponential-growth curves as "hockey-stick" curves, for the long flat growth and sudden turn upward, as this picture of a hockey stick below perfectly illustrates. | ||
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| + | <center>[[Image:HockeyStick.gif]]</center> | ||
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Revision as of 16:33, 29 September 2013
--© D. Thiebaut 08:10, 30 January 2012 (EST)
