Pizza-Cutting With Circular Arcs

Leroy Quet qq-quet at
Wed Mar 3 23:43:19 CET 2004

[Also posted to sci.math and rec.puzzles.

Instead of the typical circle-cut-by-straight-lines problem, where we 
want the maximum number of sections a circle can be cut into by n 
straight lines,
here I am asking, what is the maximum number of sections a circle can be 
divided into by n circular arcs, each arc with the same radius as the 
original circle?

I imagine a pizza of radius r being cut by a giant compass with, instead 
of a pencil, a pizza-cutter on the end, the compass having a radius of r.
And the point of this compass can be placed anywhere, either inside the 
pizza's circumference or outside it.

I get, by hand the first 2 or 3 terms:
2, 5, 9 (or 10 or more?),...
(Sequence is starting at one arc-cut.)

I am not sure, but I believe this sequence is not in the EIS.

And also, what would the sequence be if we required that the pizza/circle 
be cut so that the pieces all have the same area (but not necessarily the 
same shape)? 
Leroy Quet 

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