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The Pentadecagon


A construction that is hardly ever seen today, the construction of the pentadecagon (15 sided polygon!) is the combination of the constructions of a pentagon and triangle!

A pentadecagon has a central angle of 24°. To do this, we need to construct a 60° angle and a 36° angle, and subtract the two.
  1. Draw circle O.
  2. Draw OA and OB,so that they are perpendicular to each other, and A and B are on circle O.
  3. Find C, the midpoint of OB.
  4. Draw a circle at C (dotted) that crosses point A. Circle C crosses OB at point D.
  5. Draw a circle at A (purple), crossing point D. This circle crosses circle O at E.
  6. Draw a circle at E (blue), crossing point A. This circle crosses circle A (purple) at F.
  7. Draw a line through points O and F. OF intersects circle O at G.
  8. Draw another circle at A (cyan), this time crossing O. This new circle crosses circle O at point H.
  9. Points G and H are two points of the pentadecagon. Use them to find the rest!

© Apr. 2003 Robin Hu. All Rights Reserved.