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Re: 11-gon
Posted:
Oct 24, 1994 6:18 AM
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Michael Keyton asks:
>Since the 13-gon, 14-gon, 18-gon, 19-gon are not constructable with
>compass and straight edge, other than for linguistic curiosity, why would
>one want to name them?
(a) I can easily construct a 13-gon. Draw a circle. Pick 13 points on the
circle. Connect adjacent points. A 13-gon. (Note: the circle is only for
convenience; not strictly necessary.) However, a regular 13-gon is not
constructible.
(b) Do non-constructible polygons exist (in the mathematical sense)? I
would emphatically argue that they do, and that they *are* of interest at
least of as much interest as the 24-gon.
I feel compass-straight edge constructibility is far over-rated in
geometry. It is of a rather abstract nature; certainly one can define a
regular 13-gon and even do a pretty good of drawing one, given a protractor
or a computer. So what if you can't do a classical construction? Is this of
any great importance?
Nonetheless, a very informative discussion of names; never heard some of
these before! My students have come up with interesting suggestions (i.e,
unidecagon) but I never really knew the generally accepted terms!
g.
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