Heptagon

$\begin{figure}\begin{center}\BoxedEPSF{Heptagon.epsf}\end{center}\end{figure}$

The unconstructible regular seven-sided Polygon, illustrated above, has Schläfli Symbol $\{7\}$ .

Although the regular heptagon is not a Constructible Polygon, Dixon (1991) gives several close approximations. While the Angle subtended by a side is $360^\circ/7\approx 51.428571^\circ$ , Dixon gives constructions containing angles of $2\sin^{-1}(\sqrt{3}/4)\approx 51.317813^\circ$ , $\tan^{-1}(5/4)\approx 51.340192^\circ$ , and $30^\circ+\sin^{-1}((\sqrt{3}-1)/2)\approx 51.470701^\circ$ .

Madachy (1979) illustrates how to construct a heptagon by folding and knotting a strip of paper.

See also Edmonds' Map, Trigonometry Values Pi/7

References

Courant, R. and Robbins, H. ``The Regular Heptagon.'' §3.3.4 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 138-139, 1996.

Dixon, R. Mathographics. New York: Dover, pp. 35-40, 1991.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 59-61, 1979.