;; Homework 1 solution

;; 1. (5 points) Put the following expressions into Scheme's prefix
;; notation. Type the results into Dr. Scheme's interactions window and
;; see if you get the expected results.
;;         1. 17
;;         2. 17 * 12
;;         3. 170 * 5 * 12
;;         4. 5 * 6 * 7 * 8
;; Answer:
;; 1.
17
;; 2.
(* 17 12)
;; 3.
(* (* 170 5) 12)
;; 4.
(* (* (* 5 6) 7) 8)

;; 2. (20 points) Hand evaluate the following Scheme expressions.
;; After you are done, type them into the interactions window in Dr.
;; Scheme to confirm your results.
;;         1. (- (* 3 5) 20)
;;         2. (* pi (* 10 10))
;;         3. (+ 73 false)
;;         4. (/ 12 0)
;; Answer:
;; 1.   (- (* 3 5) 20)
;;    = (- 15 20)
;;    = -5
;;    Actual output: -5
;; 2.   (* pi (* 10 10))
;;    = (* pi 100)
;;    = approx. 314.1592653589793
;;    Actual output: #i314.1592653589793
;; 3.   (+ 73 false)
;;    = error: 'false' is not a number.
;;    Actual output: +: expects type <number> as 2nd argument, given: false; other arguments were: 73
;; 4.   (/ 12 0)
;;    = error: division by zero.
;;    Actual output: /: division by zero

;; 3. (15 points) Go to the definitions window and type in the three
;; functions from Lecture 1: owes, dough-area, and pizza-topping-area.
;; Click the execute button. Go to the interactions window, and invoke 
;; each function on two different arguments. Hand in your code, your 
;; tests and the results.
;;
;; Answer:
;; (Note: the contracts are not technically required for this problem.
;; They will be required in future homework.)

;; owes: number --> number
;; [purpose from lecture]
;;
(define (owes p)
  (* 12 (/ p 8)))

;; dough-area: number --> number
;; [purpose from lecture]
;;
(define (dough-area r)
  (* pi (* r r)))

;; pizza-topping-area: number --> number
;; [purpose from lecture]
;;
(define (pizza-topping-area d)
  (dough-area (- (/ d 2) 1)))

; Examples:
; (Note: These are my examples.  You are free to use whatever values you want.)
(owes 10)
15
(owes 1)
1.5

(dough-area 5)
#i78.53981633974483
(dough-area 0)
0

(pizza-topping-area 12)
#i78.53981633974483
(pizza-topping-area 1000000000000000)
#i7.85398163397445e+029

;; 4. (10 points) Write a function Rectangle-area that consumes a height 
;; and a width, and produces the area of a rectangle of that size. Be 
;; sure to write down the contract and purpose. Test your program on 
;; several inputs. Hand evaluate the expression (Rectangle 10 15).

;; Answer:

;; Rectangle-area: number number --> number
;; Return the area of a rectangle with dimensions height x width.
;; [Not required: The units of the return value are of course
;;  square-units of whatever units the inputs were measured in.]
;;
(define (Rectangle-area height width)
  (* height width))

; Tests:
; Again, your test don't have to be exactly what's shown here, but
; you should test a wide range of values.
(= (Rectangle-area 2 50)
   100)
(= (Rectangle-area 5 4)
   20)
(= (Rectangle-area 20 0)
   0)
(= (Rectangle-area 1 14)
   14)

;; Hand evaluation:
;;   (Rectangle-area 10 15)
;; = (* 10 15)
;; = 150