Image:Bertrand1-scatterplot.jpeg

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Bertrand1-scatterplot.jpeg‎ (288 × 288 pixel, file size: 17 KB, MIME type: image/jpeg)

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.
Subject to disclaimers.

This image is licensed under the Creative Commons
Attribution ShareAlike License v. 2.0:
http://creativecommons.org/licenses/by-sa/2.0/

File history

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(del) (cur) 04:42, 21 August 2004 . . Wile E. Heresiarch (Talk | contribs) . . 288×288 (17,651 bytes) (Bertrand's paradox -- distribution of midpoints of chords chosen at random, solution 1)