Geometric Constructions of Regular N-Gons Wednesday, April 4, 2007

**How do you construct a regular octagon given:

• The Width
• An apothem
• A side
• A segment from the center to a vertex

By the width of apothem (one construction):

A segment from center to the vertex:

Continuing – extending the previous construction:

Construction given a width:

**Can you find any golden ratios within the construction of an octagon?

New Problem (“Exploration of a problem with two squares”):

What is the ratio of the big square to the small, yellow “square”?

Using more parallel lines can provide a “grid” for students to have a better visual idea as to how much this is:

How might that change if we weren’t using the midpoints, but rather points 1/3 or 1/4 of the way down instead of half way down?