How many sides does a circle have?
My son answered "infinate" on a test and was corrected. The school insists the answer is 0.
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 up-side and a down-side. 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 n-sided regular polygon, then one can justify the answer that
the circle has infinitely many infinitesimal sides. Our conclusion:
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
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