Math CentralQuandaries & Queries


Question from RINA, a parent:

My questions is : would a vertices and sides of a polygon be the same number.  For example, a octagon it has 8 points and 8 sides. Am i correct?

Yes, well spotted! A rigorous proof may be obtained by noting that if we pair each edge with the point on (say) its clockwise end, the pairing is one-to-one, which is more or less the definition of same-size set.

In three or more dimensions it is of course more complicated!
The relation there is something called Euler's formula:

vertices + faces = edges + 2

Good Hunting!


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