Einstein's Cat
- 182
- 2
With the lonely runner conjecture, can the runners run along a circular track of any diameter or does the conjecture require that they run along a unit circle?
The lonely runner conjecture of Wills and Cusick, in its most popular formulation, asserts that if n runners with distinct constant speeds run around a unit circle ##\mathbb{R}/\mathbb{Z}## starting at a common time and place, then each runner will at some time be separated by a distance of at least ##1/(n+1)## from the others. In this paper we make some remarks on this conjecture.