File:ExtremeValueTheorem.png
Summary
| Description | |
| Date | 21 January 2007 (original upload date) |
| Source |
I generated the function with the Python script: #!/usr/bin/python
from random import *
k = 0
for i in xrange(1000000):
k += gauss(0, 1)
print i, k
I redirected the output to a file, then I plotted it with gnuplot with: set term png size 6000,4500 set out 'out.png' pl [][-600:700] 'randfunc.txt' w p ps 3 pt 7 ps 3 pt 7 gives circular dots of 17 pixels in diameter. The high number of samples caused them to overlap, forming a continuous line. (Actually, in the places where the function happened to change very quickly, there were gaps between them, but in the downscaled version they are not evident.) Then I used GIMP to change the color of the graph, add a blue and a green dot at the bottom and the top, Gaussian blur it at 2 pixels, and downscale it to its current size with cubic interpolation. |
| Author | Army1987 at English Wikipedia |
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Army1987 at English Wikipedia, the copyright holder of this work, hereby publishes it under the following licenses:
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| Attribution: Army1987 at English Wikipedia | ||
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Original upload log
The original description page was here. All following user names refer to en.wikipedia.
| Date/Time | Dimensions | User | Comment |
|---|---|---|---|
| 2008-01-22 13:50 | 1300×975× (125578 bytes) | Army1987 | A continuous function. |
| 2008-01-21 23:54 | 1300×975× (157979 bytes) | Army1987 | A continuous function, showing the extreme value theorem. The maximum is shown in green and the minimum in blue. I generated it with this Python script: <syntaxhighlight lang="Python"> #!/usr/bin/python from random import * k = 0 for i in range(100000): k += |
| 2007-01-21 20:18 | 300×150× (9309 bytes) | Army1987 | A [[continuous function]] on a closed interval, showing the [[extreme value theorem]]. The function is the integral of a piecewise continuous function which, on each one of 256 very small interval, takes a normally distributed randomly choosen value. I p |