a. Consider the following 13-by-13 square. Notice the square has been divided into p...

a. Consider the following 13-by-13 square. Notice the square has been divided into polygons with dimensions that are consecutive Fibonacci numbers. What is the area of the square?

b. If the square from part (a) is cut along the lines and rearranged to form the following rectangle, what is its area? What happened?

c. All of the lengths used in parts (a) and (b) are Fibonacci numbers. What happens if you replace the lengths from part (a) with the consecutive Fibonacci numbers 8, 13, and 21? Draw the resulting square and rectangle. Calculate the areas of both the square and the rectangle. What happened?

d. Select another set of three consecutive Fibonacci numbers and construct the corresponding square and rectangle. How do their areas compare?

e. If the lengths used in the creation of the square and rectangle are 1, φ, and φ + 1, rather than 5, 8, and 13, what happens to the areas? Use the fact that