(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.

Awesome stuff, Harry. I'd love to display that image in the MArTH Gallery. Great use of color. Are you totally happy with it, or would you want to reproduce the design?

ReplyDeleteHave you played around with this in Processing?