(Sorry for the resolution, the file size was too big for my more detailed scan)
The other night I made this shape. As you can see, it is 4 regular polygons inside of each other all sharing the same side length.
I constructed everything with only compass and straightedge, except for the pentagon and hexagon sides coming out of from the base. For the other 2 (or 3) sides of the pentagon/hexagon I copied the angle of the first two lines coming from the base.
Methods used in this construction.
- Copying lengths and angles
- Making an equilateral triangle
- Erecting a perpendicular (for the square, because it has 90 degree interior angles)
To do list
- Explain why pentagons and hexagons have interior angles of 108 and 120 degrees respectively, as well as give proof for a general case for any regular polygon
- Describe how to execute the 3 methods listed above
P.S. Those two purple crayon smudges are driving me crazy.