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Re: 11-gon
Posted:
Oct 26, 1994 9:27 PM
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1. Doesn't the Susan B. Anthony $1 coin have an "inscribed" regular
hendecagon on it and is not itself a regular hendecagon? Regular
hendecagon coins include the Canadian "loonie" $1 coin as well as the
Canadian penny.
2. Maybe I'm just a naive high school geometry teacher, but I think that
the non-straightedge/compass constructible regular polygons are very
interesting. My recollection is that Gauss proved (at age 18?) that a
regular n-gon can be straightedge/compass constructible if n is a prime
Fermat number or the product of different prime Fermat numbers. I would
think that this would then put the non-constructibles into an interesting
class of numbers. This also leads to some amazing attempts to construct
the regular 17-gon (see Sci Am., and Rouse-Ball/Coxeter "Mathematical
Recreations and Essays"). Maybe my lack of background/sophistication in
pure math research may account for such continual awe and wonder of this
result linking number theory and geometry, but then again, as I recall,
this result was also worthy of inclusion in his 1801 Disquisitiones
Arithmeticae. This is a story which I relate with excitement to my high
school geometry students. However, with the tenor of the e-mail postings
regarding constructions, maybe it's not the big deal that I thought it
was...
In provincial wonderment,
Dave Masunaga
Iolani School
563 Kamoku St.
Honolulu HI 96826
(808)949-5355
On Sun, 23 Oct 1994, Michael Keyton wrote:
> An elderly acquaintance of mine who recently celebrated his 100th
> birthday used the phrase "lexicographical heteromorphs" for these
> linguistic abominations that use mixed roots. Undecagon and duodecagon
> are such in that they unite Latin prefixes with Greek suffices.
> A subsequent reply correctly gives hendecagon for 11 sides and dodecagon
> for 12. Also the Susan B. Anthony $1 coin for the U.S. was in the shape
> of a regular hendecagon. These still exist, but are rarely seen in
> circulation.
> 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? However, what name does one give to the 24-gon,
> the 48-gon, and the 96-gon; those polygons which were useful in the early
> approximations of PI?
>
> Michael Keyton
> St. Mark's School of Texas
>
>
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