# A conjecture on iterated circumcentres

**Conjecture**Let be a sequence of points in with the property that for every , the points are distinct, lie on a unique sphere, and further, is the center of this sphere. If this sequence is periodic, must its period be ?

Luis Goddyn discovered this curiosity, and proved the above conjecture for . He also studied related sequences, for instance, the sequence in where the point is the circumcentre of the points with index , , and . See Iterated Circumcenters for a delightful and interactive discussion of this problem.

## Bibliography

*[G] Luis Goddyn, Iterated Circumcenters

* indicates original appearance(s) of problem.