[FOM] The regular heptadecagon

Jesse Alama alama at stanford.edu
Mon Aug 13 20:09:07 EDT 2007

Thomas Forster <T.Forster at dpmms.cam.ac.uk> writes:

>  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...?



I found several references concerning the heptadecagon.  Although Gauss'
original proof uses methods that might be unintelligible to ancient
mathematicians, one of the references on the Mathworld page
(R. C. Archibald, "Gauss and the regular polygon of seventeen sides",
American Mathematical Monthly 27, 1920, pp. 323-6) mentions some known
synthetic (rather than algebraic) constructions.  I assume that such
constructions would be intelligible to an ancient Greek geometer.


Jesse Alama (alama at stanford.edu)

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