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| Math Central | Quandaries & Queries |
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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!
RD
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