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 > >