On the Traveling Fly Problem

• Published in 1996
• Added on 2025-04-22

Gargano, LoSacco and Gargano have studied the following problem: "if a fly starts at a random point inside a sphere of radius \(R^n\) and flies in a straight line in a random direction until it reaches the boundary, what is the average distance the fly travels?" They gave exact answers for \(n=1,2,3\) and approximate answers for \(4 \leq n \leq 9\), leaving the general case as an open problem. This problem is solved here.

Comment

The solution uses the fractions \(n/( (n-1)/( (n-2)/.... 1)))) \), which feels unexpected.

Links

• https://www2.math.uu.se/~svantejs/papers/sj114.pdf

Other information

BibTeX entry

@article{OntheTravelingFlyProblem,
	key = {OntheTravelingFlyProblem},
	type = {article},
	title = {On the Traveling Fly Problem},
	author = {Svante Janson},
	abstract = {Gargano, LoSacco and Gargano have studied the following problem: "if a fly starts at a random point inside a sphere of radius \(R^n\) and flies in a straight line in a random direction until it reaches the boundary, what is the average distance the fly travels?"
They gave exact answers for \(n=1,2,3\) and approximate answers for \(4 \leq n \leq 9\), leaving the general case as an open problem. This problem is solved here.},
	comment = {The solution uses the fractions \(n/( (n-1)/( (n-2)/.... 1)))) \), which feels unexpected.},
	date_added = {2025-04-22},
	date_published = {1996-04-22},
	urls = {https://www2.math.uu.se/{\~{}}svantejs/papers/sj114.pdf},
	collections = {animals,easily-explained,fun-maths-facts},
	url = {https://www2.math.uu.se/{\~{}}svantejs/papers/sj114.pdf},
	urldate = {2025-04-22},
	year = 1996
}