[FOM] The regular heptadecagon
Ian Grant
Ian.Grant at cl.cam.ac.uk
Mon Aug 13 06:26:44 EDT 2007
On Sun, 12 Aug 2007 08:15:28 +0100 (BST)
Thomas Forster <T.Forster at dpmms.cam.ac.uk> wrote:
> A question came up in a seminar here the other day.... Gauss'
> construction of the regular heptadecagon (17 sides) by compass
> and straightedge. Would a classical Greek, on being shown this
> construction, be able to see that the figure thus constructed
> was indeed a regular heptadecagon...?
What a lovely question. According to http://mathworld.wolfram.com/Heptadecagon.html Gauss only proved it was constructible, he didn't actually produce a construction. That was first done by Erchinger some 4 years later. However the same page gives a construction by Richmond and comments "Both Richmond's and Tietze's constructions require extensive calculations to prove their validity."
It is vaguely suggested that Richmond proved his construction was sound, so perhaps this would help decide:
Richmond, H. W. "A Construction for a Regular Polygon of Seventeen Sides." Quart. J. Pure Appl. Math. 26, 206-207, 1893.
Ian
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