
Re: 11gon
Posted:
Oct 24, 1994 6:18 AM


Michael Keyton asks: >Since the 13gon, 14gon, 18gon, 19gon 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 13gon. Draw a circle. Pick 13 points on the circle. Connect adjacent points. A 13gon. (Note: the circle is only for convenience; not strictly necessary.) However, a regular 13gon is not constructible.
(b) Do nonconstructible 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 24gon.
I feel compassstraight edge constructibility is far overrated in geometry. It is of a rather abstract nature; certainly one can define a regular 13gon 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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