
How many sides does a circle have?
My son answered "infinate" on a test and was corrected. The school insists the answer is 0.
Thanks,
georganne
Hi Georganne,
There are two sources of ambiguity here.
 The word CIRCLE sometimes refers to a circular disk (because it is
common to talk about "the area of a circle"), but often the word refers
only to the boundary of the disk (namely, the points that are equally
distant from the point at the center of the figure).
 The meaning of the word SIDE depends on its context. A polygon in the
plane has, by definition, n vertices and each pair of consecutive vertices
are joined by a side. It is clear that a polygon with n vertices has n
sides. In general, the word side depends on the dimension of the figure 
a side is always part of the boundary.
So what is the side of a circle? If you think of the circle as a
disk then it it has an upside and a downside. If you think of it as a
curve, then it has an inside and an outside. If you think of it as the
limit of an nsided regular polygon, then one can justify the answer that
the circle has infinitely many infinitesimal sides. Our conclusion:
the
question, "How many sides does a circle have?", is too ambiguous to have a definite answer.
Perhaps the appropriate response is "there is no natural way of saying what the side of a circle is."
Chris and Harley
Go to Math Central

