Carl Friedrich Gauss was born April 30, 1777 and when he was 19 years old, he proved that there was a way to construct a 17 sided regular polygon with only a compass and straight edge–something that escaped the ancient Greek mathematicians. This is how it is done:

- Draw a circle around point O.
- Draw a diameter to form a Semicircle P
_{0 } - Find the perpendicular of OP
_{0}and call it OB - Find J a quarter the way up OB (bisect OB a couple of times)
- Join JP
_{0}to form < OJP - Find E so that < OJE is a quarter of < OJP (Bisect is a couple of times)
- Find F so the < EJF is 45° (bisect a perpendicular)
- Construct a semicircle from F to P
_{0}(bisect FP_{0}to find the center of the semicircle) - Find point K at the place this semicircle cuts across OB.
- Draw semicircle with center E and radius EK
- This cuts the extension of OP
_{0}at N_{3}and N_{5 } - Draw the perpendiculars through N
_{3}and N_{3}to find P_{3}and P_{5 } - P
_{0}, P_{3}, P_{5}are the original, third and fifth points of the Heptagon.

Can you find a way to discover half the distance between P_{3} and P_{5 } so you get the single length of one side? If you can then you can draw all 17 equal sides!