EMAT 6700
"The Greeks claimed that the creations of nature and art
owed their beauty to certain underlying mathematical patterns. One of these
was the law of the golden mean," or golden ratio. (Olds)
How would you make a golden rectangle?
First draw a square, ABCD, then find the midpoint of segment
AB. Connect m to point D. Use mD as the radius of a circle
and find where the extension of AB intersects the circle at point F.
Draw a perpendicular line at point F and extend CD until it intersect at
point E. The ratio of y/x = x/(x + y).
For an interactive image go here.
Here is an interesting puzzle that uses some of the ideas
of the golden ratio and the Fibonacci numbers. The idea is to take
the different geometric shapes and rearrange them into a rectangle.
The pieces are divided using the measurements 3 and 5. Go here
to try it. (solution) (Algebraic
exploration)
