Thursday, June 01, 2017

[ueajojfc] Best 17-gon star

The regular 17-gon is quite epic as a constructible figure, but it looks too similar to a circle.  A star drawn among the vertices avoids this problem and also demonstrates 17-fold symmetry.  There are many possible stars among 17 points; which one is best?

The Gauss monument in Braunschweig uses the star with narrowest possible points.


Aesthetically attractive might be the star with nearly right angle points, probably connecting every 4th vertex.  This may highlight how 17 is 1 greater than 16, a multiple of 4.

Draw a design on the face of the star that helps quickly recognize that the star has 17 points.  This might be easy by only requiring bilateral symmetry, with one point treated differently.  Can it be illustrated that 17 is a Fermat number?

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