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Topic: What's a 9,11,12,etc-sided figure called?
Replies: 38   Last Post: Dec 16, 2010 10:17 AM

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 NealAgMan@aol.com Posts: 181 Registered: 12/4/04
Re: What's a 9,11,12,etc-sided figure called?
Posted: May 30, 2006 4:33 PM

Did you know (I'm sure you did at one point) that a regular decagon can be inscribed in a circle? It turns out that if the radius of the circle is divided into mean-extreme ratio, the larger segment is congruent to the side of the inscribed regular decagon.

Then to inscribe a regular pentagon, of course, one just joins alternate vertices of the inscribed regular decagon.

Now we can prove (or would you rather "conjecture") that a regular pentadecagon can be inscribed in a circle, since we have now have ways of constructing arcs of measure 60 and 36 degrees (by inscribing a regular hexagon and a regular decagon in a circle). Their difference, an arc of measure 24 degrees, is the arc cut off by the side of the regular 15-gon. <------------------------------------(this 19th century geometry person is now off to practice the minuet)----------------<

Date Subject Author
8/24/97 J. Stefanek
8/25/97 Sarah Seastone
10/9/03 geoffy
10/12/03 Ken.Pledger@vuw.ac.nz
10/13/03 John Conway
10/13/03 me@talmanl1.mscd.edu
10/13/03 Ed Wall
10/13/03 Mary Krimmel
10/13/03 Steve Earth
10/14/03 John Conway
5/3/06 brandon park
5/27/06 bgormalley@gmail.com
12/8/03 chris
12/12/03 Eur Ing Panagiotis Stefanides
11/25/03 india
3/8/04 tyesha
1/8/04 Lavonte Smith
1/19/04 Dr. Bluca
1/20/04 John Conway
9/17/04 Laike
5/3/06 brandon park
5/3/06 brandon park
3/22/04 Alex Hebert
3/23/04 Mary Krimmel
8/25/97 J. Stefanek
8/25/97 John Conway
12/3/03 Eur Ing Panagiotis Stefanides
12/2/03 Lauren
4/16/07 Paris
2/6/08 ???
2/25/08 K. E. Pledger
3/6/08 xamcire
12/16/10 chase
3/7/04 Jack
5/30/06 NealAgMan@aol.com
5/30/06 Joshua Zucker
5/30/06 NealAgMan@aol.com
2/26/08 Rich Kleinschmidt
2/27/08 K. E. Pledger