Homework due Monday, January 13th

1. Given that F₃₀=832,040 and F₃₁=1,346,269, find the next five terms in the Fibonacci sequence and use them to get better approximations for the golden ratio.
2. Consider altering our construction method for a golden rectangle in the following ways
   • instead of using the middle of the bottom side of the square, use a point three-quarters of the way from the left
   • instead of using the middle of the bottom side of the square, use a point two-thirds of the way from the left
   Draw a picture for each construction and, like in class, use algebra to find the ratio of the longer side to the shorter.
3. Suppose you start with a golden rectangle. Use algebra to show that the following procedures will produce more golden rectangles:
   • fold the original golden rectangle in half vertically and then horizontally
   • add a square to one side of the original golden rectangle

Last updated: 1/7/03