The Heptadecagon

The Heptadecagon (17 sided polygon), is one of a handful of prime numbers that can be constructed. A triangle and pentagon are two others. There are known constructions for the 257-gon and 65537-gon! German mathematician Karl Gauss proved its construction in 1796!

  1. Draw a circle centered at O (yellow).
  2. Draw OA and OB so that they are perpendicular to each other. Points A and B should be on circle O.
  3. Find point C on OA, so that OC is 1/4 of OA.
  4. Find point D on line OB, so that angle OCD is 1/4 of angle OCB.
  5. Find point E on extended line OB, so that the angle ECD is 45°.
  6. Do this part carefully! Find the midpoint F of EB.
  7. Draw a circle at F (dotted) crossing B. Circle F (dotted) intersects OA at G.
  8. Draw a circle at D (purple) crossing G. This circle crosses the extended line OB at H.
  9. At points F and H draw a perpendicular line (cyan) intersecting circle O at points I and J.
  10. Points I, J, and B are points of the heptadecagon. Use them to find the other 14 points!

© Apr. 2003 Robin Hu. All Rights Reserved.