All Questions
4 questions
9
votes
1
answer
338
views
Visibility in a growing orchard
This is a variant on Polya's orchard problem.1,2
Suppose trees are planted randomly in the plane.
The question is: How many trees are visible from the origin as
their radii grow?
More precisely, ...
- 151k
3
votes
0
answers
144
views
What is the probability that these four random areas can yield a tetrahedron?
This is inspired by this problem about randomly broken sticks that can form a triangle. It goes in a different direction than this generalization about randomly broken sticks that can form a ...
- 13.4k
6
votes
1
answer
273
views
Proof of a statement from Steele's "Probability theory and combinatorial optimization"
I am reading "Probability theory and combinatorial optimization" by J.M. Steele and am hung up on a statement made in Section 2.2 of Chapter 2, "Easy size bounds", in which it is stated (paraphrasing ...
2
votes
1
answer
121
views
Expected length of a certain kind of nearest-neighbor graph
Suppose I have sets of points $Z_1,\dots,Z_N$, such that $|Z_i|=m$ for all $i$, and where all $m\times N$ points are independently distributed uniformly at random in the unit square. Can someone give ...