15Dec/119
From “God Plays Dice,” an interesting geometry problem
Here's a cute problem (from Robert M. Young, Excursions in Calculus, p. 244): "What is the average straight line distance between two points on a sphere of radius 1?"
(Answer to follow.)
Note the number of comments with different answers.
"Excursions in Calculus," from what I could see at Google Books, looks like it has many interesting problems.
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December 16th, 2011 - 21:12
square root of 2?
December 17th, 2011 - 23:19
8/pi^2 ?
January 1st, 2012 - 06:42
Integral of 2cosxsin2x x varying from 0 to 90 degrees
= -4t^2dt t varying from 1 to 0
= 4/3
January 1st, 2012 - 06:43
4/3
January 1st, 2012 - 10:51
I have games on my blog much simpler if you want to solve some, appear.
Greetings pekota.
January 1st, 2012 - 18:28
The answer is 2/3, being the average chord length between any 2 points on a circle of radius 1.
January 30th, 2012 - 15:30
This is a quite fun problem indeed.
1/4π ∫[0->π] (2π sinθ)(2sinθ/2) dθ = 4/3
Here’s my blog post explaining why this is so:
http://logics.ant-ti.com/a-geometric-probability-problem/
Have you guys thought what is the average straight line distance between two points on an unit n-sphere?
February 2nd, 2012 - 08:57
I found this enlightening:
February 13th, 2012 - 04:18
The answer is the volume divided by the area of the sphere:
(4/3 π r³) / (2 π r²) = 2 / 3 r