Can you construct a regular heptagon

Washington, DC: Math. Bankoff, L. Monthly 62 , , Bold, B. New York: Dover, pp. Conway, J. The Book of Numbers. New York: Springer-Verlag, pp. Courant, R. Oxford, England: Oxford University Press, pp. Dixon, R. Finlay, A. Heath, T. A Manual of Greek Mathematics. Oxford, England: Clarendon Press, pp. Johnson, C. Madachy, J. Madachy's Mathematical Recreations.

Wells, D. London: Penguin, p. Keep in mind that you will need some extra space around the circle for construction lines. Use your compass to trace the distance BD around the circle. You should end up exactly where you started. There is an error of about. If you don't end up exactly where you started, there were probably some inaccuracies with the construction tools e.

See Construct a Regular Pentagon. Yes No. Not Helpful 13 Helpful Include your email address to get a message when this question is answered. Put a piece of cardboard or a book under your paper so your compass doesn't slip. Helpful 3 Not Helpful 1. Helpful 2 Not Helpful 1. Submit a Tip All tip submissions are carefully reviewed before being published. Since 7 cannot be written as the product of a power of two and a Fermat prime, it is impossible to do an exact compass and straightedge construction of a heptagon.

However, the above method has an error of less than. Here, the complex numbers in the numerator, when added, cancel out each other's imaginary parts leaving behind a real expression.

Note that you CANNOT get rid of the complex numbers in the numerator, as the minimal polynomial that I pointed out earlier is casus irreducibilis. And it doesn't end there. In fact, when dividing arbitrary angles into anything that isn't a power of two, a lot of times you will end up having to take cube roots, 5th roots, 7th roots, et cetera of complex numbers, which you cannot remove from the expression without introducing trigonometric functions. Sign up to join this community.

The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Is it possible to construct a regular heptagon with just compass and straightedge? Ask Question. Asked 4 years, 9 months ago. Active 4 months ago. Viewed 5k times.