Difference between revisions of "CSC103: DT's Notes 1"
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The left column represents the number of the square being covered, and this number increases by 1 every time. The second column represents the quantity of interest, the number of grains, and doubles every time. So that is the setup for studying our exponential growth: something that doubles in size every fixed interval, in our case every new square. | The left column represents the number of the square being covered, and this number increases by 1 every time. The second column represents the quantity of interest, the number of grains, and doubles every time. So that is the setup for studying our exponential growth: something that doubles in size every fixed interval, in our case every new square. | ||
| − | Let's plot these numbers to | + | Let's plot these numbers to observe their growth (plots generated with [[CSC103 Plotting with R|R]]). |
<br /> | <br /> | ||
| − | <center>[[Image:CSC103_ExponentialGrowth1.png| | + | <center>[[Image:CSC103_ExponentialGrowth1.png|450px]]</center> |
<br /> | <br /> | ||
| − | Note the quick growth of the | + | Note the quick growth of the squares. 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: |
<br /> | <br /> | ||
<center> | <center> | ||
| − | [[Image:CSC103_ExponentialGrowth2.png| | + | [[Image:CSC103_ExponentialGrowth2.png|250px]] |
| − | [[Image:CSC103_ExponentialGrowth3.png| | + | [[Image:CSC103_ExponentialGrowth3.png|250px]] |
| − | [[Image:CSC103_ExponentialGrowth4.png| | + | [[Image:CSC103_ExponentialGrowth4.png|250px]] |
</center> | </center> | ||
| + | |||
| + | <br /> | ||
| + | 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 (1, 2, 3, etc) is completely obfuscated by the large size of the quantities associated with the squares of higher order. | ||
| + | |||
| + | 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. | ||
| + | |||
Revision as of 16:08, 29 September 2013
--© D. Thiebaut 08:10, 30 January 2012 (EST)
