File:ExtremeValueTheorem.png
Original file (1,300 × 975 pixels, file size: 123 KB, MIME type: image/png)
Captions
Summary
[edit]DescriptionExtremeValueTheorem.png | |
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 |
Licensing
[edit]This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Subject to disclaimers. | ||
Attribution: Army1987 at English Wikipedia | ||
| ||
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Original upload log
[edit]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 |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:17, 21 September 2016 | 1,300 × 975 (123 KB) | OgreBot (talk | contribs) | (BOT): Reverting to most recent version before archival | |
22:17, 21 September 2016 | 1,300 × 975 (154 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2008-01-21 23:54:48 by Army1987 | ||
22:17, 21 September 2016 | 300 × 150 (9 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2007-01-21 20:18:53 by Army1987 | ||
19:20, 21 September 2016 | 1,300 × 975 (123 KB) | Milicevic01 (talk | contribs) | Transferred from en.wikipedia |
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Horizontal resolution | 28.35 dpc |
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Vertical resolution | 28.35 dpc |
File change date and time | 13:45, 22 January 2008 |