
Re: 11gon
Posted:
Oct 26, 1994 9:27 PM


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 nonstraightedge/compass constructible regular polygons are very interesting. My recollection is that Gauss proved (at age 18?) that a regular ngon 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 nonconstructibles into an interesting class of numbers. This also leads to some amazing attempts to construct the regular 17gon (see Sci Am., and RouseBall/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 email 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)9495355
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 13gon, 14gon, 18gon, 19gon 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 24gon, > the 48gon, and the 96gon; those polygons which were useful in the early > approximations of PI? > > Michael Keyton > St. Mark's School of Texas > >

