Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with half-open arcs, but not with open arcs. They also showed that the plane can be covered with congruent closed and half-open segments, but not with open ones.

# Mikusiński's Problem

## See also

Great Circle, Sphere## Explore with Wolfram|Alpha

## References

Conway, J. H. and Croft, H. T. "Covering a Sphere with Great-Circle Arcs."*Proc. Cambridge Phil. Soc.*

**60**, 787-900, 1964.Gardner, M. "Point Sets on the Sphere." Ch. 12 in

*Knotted Doughnuts and Other Mathematical Entertainments.*New York: W. H. Freeman, pp. 145-154, 1986.

## Referenced on Wolfram|Alpha

Mikusiński's Problem## Cite this as:

Weisstein, Eric W. "Mikusiński's Problem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MikusinskisProblem.html