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?