Constructing the Heptadecagon
- Lamberto Lamberti
Draw a circle centered at O, and choose one vertex V on the circle. Then locate the point A on the circle such that OA is perpindicular to OV, and locate point B on OA such that OB is 1/4 of OA. Then locate the point C on OV such that angle OBC is 1/4 the angle OBV. Then find the point D on OV (extended) such that DBC is half of a right angle.Let E denote the point where the circle on DV cuts OA. Now draw a circle centered at C through the point E, and let F and G denote the two points where this circle strikes OV. Then, if perpindiculars to OV are drawn at F and G they strike the main circle (the one centered at O through V) at points V3 and V5, as shown below:The points V, V3, and V5 are the zeroth, third, and fifth ertices of a regular heptadecagon, from which the remaining vertices are easily found (i.e., bisect angle V3 O V5 to locate V4, etc.).