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

 

 

 

**How do you construct a regular octagon given:

 

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?