# Wild About Math!Making Math fun and accessible

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?"

"Excursions in Calculus," from what I could see at Google Books, looks like it has many interesting problems.

1. square root of 2?

2. 8/pi^2 ?

3. Integral of 2cosxsin2x x varying from 0 to 90 degrees
= -4t^2dt t varying from 1 to 0
= 4/3

4. I have games on my blog much simpler if you want to solve some, appear.
Greetings pekota.

5. The answer is 2/3, being the average chord length between any 2 points on a circle of radius 1.

6. 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?

7. I found this enlightening: