Saturday's Exercises

Exercise 1:

Write two procedures that use the following definitions to convert
days into minutes and minutes into days:

(define seconds-per-minute 60.0)
(define minutes-per-hour 60.0)
(define hours-per-day 24.0)
(define days-per-year 365.25)

(days->minutes 1)
;Value: 1440.0
(minutes->days 1)
;Value: 0.0006944444444444445

Exercise 2:

A number is called Wondrous if it passes the following test:
If the number is odd, we triple it, add 1, and test the result.
If the number is even, we divide it by two and test the result.
If the number ever reaches 1, it's wondrous.

Finish the following procedure definition to determine if the input
number is wondrous.

(define wondrous?
  (lambda (n)
     (display n)
     (newline)
     your-code-here))

Lambda bodies are allowed to contain multiple expressions.  When
applied, the evaluator evaluates the expressions in order and returns
the value of the last.  If you fill in 1 for your-code-here, the
procedure would print out the value of n on a line by itself and
return 1.  If you fill in a correct answer:

(wondrous? 3)
3
10
5
16
8
4
2
1
;Value: #t

Try testing a couple of other numbers, like 15 or 27.

Exercise 3:

A variant on the fibonacci sequence, but more chaotic can expressed:
Q(n) = Q(n-Q(n-1)) + Q(n-Q(n-2))
Q(1) = Q(2) = 1

Write a procedure that computes Q.  Find out the first 10 or so
numbers of the sequence.

(Q 5)
;Value: 3
(Q 18)
;Value: 11