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Re: What's a 9,11,12,etc-sided figure called?
Posted:
May 30, 2006 4:33 PM
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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)----------------<
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