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 (ÒExploration of a problem with two squaresÓ):

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

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

How
might that change if we werenÕt using the midpoints, but rather points 1/3 or
1/4 of the way down instead of half way down?