### Suggested Projects

1. Explain Archimedes' trisection of the angle.

2. Explain the determination of the latitude.

3. Find all of the angles in a pentagram.

4. Show how the proportion of the golden mean arises in the pentagram.

5. Explain the construction of the proportion of the golden mean.

6. Explain the construction of the pentagram.

7. Show how to use a golden rectangle to construct a pentagram.

8. Explain Thales of Miletus' determination of the distance of a ship from the shore.

9. Prove that the deflection angle between the tangent to a circle and a chord to another point on the circle is half of the central angle determined by the chord.

10. Answer the feet in the mirror question.

11. Explain the construction of an octagon by cutting off corners of a square.

12. Explain the construction of a dodecagon by cutting off corners of a regular hexagon.

13. Explain the construction of a decagon by cutting off corners of a regular pentagon.

14. Explain the generic construction of a regular 2n-gon by cutting off the corners of a regular n-gon.

15 Prove the Pythagorean Theorem.

16. Snell's Law.