Tuesday's Exercises:

Exercise 1:

Write a procedure that when given a width, returns the length of the
most beautiful rectangle having that width.  According to studies, the
most beautiful rectangle is one whose ratio of length to width is the
golden ratio.  The golden ratio can be most easily be expressed as
(sqrt(5)+1)/2.

(beautiful-rectangle 1)
;Value: 1.618033988749895
(beautiful-rectangle 34.5)
;Value: 55.82217261187137

Exercise 2:

Write a procedure that when given a number, determines if it is the
square of an integer without using the sqrt procedure.  You'll most
likely want to write a helper procedure that takes the number and
"current integer", checks to see if the current integer squared is the
number, and continues on based on the result of the check.

(is-square? 4)
;Value: 2
(is-square? 7)
;Value: #f
(is-square? 256)
;Value: 16

Exercise 3:

Write a procedure that when given a number n, returns the nth prime.
Assume that the 0th prime is 2.  You'll also want to write a helper
procedure for this exercise too.

(nth-prime 0)
;Value: 2
(nth-prime 1)
;Value: 3
(nth-prime 2)
;Value: 5
(nth-prime 12)
;Value: 41