File:Bertrand1-scatterplot.jpeg

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Bertrand's paradox -- distribution of midpoints of chords chosen at random, solution 1

This image is an original work by Robert Dodier (User:Wile E. Heresiarch).

Here are the commands (of the R programming language) by which this image was created.

n <- 10000

r1 <- runif (n) * 2 * pi
r2 <- runif (n) * 2 * pi

x1 <- cos (r1)
y1 <- sin (r1)

x2 <- cos (r2)
y2 <- sin (r2)

x <- (x1 + x2)/2
y <- (y1 + y2)/2

z <- sqrt(x^2+y^2)
sum(z<1/2)

plot (x, y, pch='.', col='red')
dev2bitmap (file='bertrand1-scatterplot.jpeg', type='jpeg',
 res=288, height=8, width=8)

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

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	You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
	This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue

This file is licensed under the Creative Commons Attribution-Share Alike 2.0 Generic license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/2.0CC BY-SA 2.0 Creative Commons Attribution-Share Alike 2.0 truetrue

Original upload log[edit]

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.

Click on date to download the file or see the image uploaded on that date.

• (del) (cur) 04:42, 21 August 2004 . . en:User:Wile_E._Heresiarch Wile E. Heresiarch ( en:User_talk:Wile_E._Heresiarch Talk) . . 288x288 (17651 bytes) (Bertrand's paradox -- distribution of midpoints of chords chosen at random, solution 1)