001.rkt

#lang htdp/bsl

; Exercise 1.
; -----------
; Add the following definitions for x and y to DrRacket’s definitions area:
;
;     (define x 3)
;     (define y 4)
;
; Now imagine that x and y are the coordinates of a Cartesian point. Write down
; an expression that computes the distance of this point to the origin, that
; is, a point with the coordinates (0,0).
;
; The expected result for these values is 5, but your expression should produce
; the correct result even after you change these definitions.
;
; Just in case you have not taken geometry courses or in case you forgot the
; formula that you encountered there, the point (x,y) has the distance
;
;    (x^2 + y^2)^(1/2)
;
; from the origin. After all, we are teaching you how to design programs, not
; how to be a geometer.
;
;
; To develop the desired expression, it is best to click RUN and to experiment
; in the interactions area. The RUN action tells DrRacket what the current
; values of x and y are so that you can experiment with expressions that
; involve x and y:
;
;    > x
;    3
;    > y
;    4
;    > (+ x 10)
;    13
;    > (* x y)
;    12
;
;
; Once you have the expression that produces the correct result, copy it from
; the interactions area to the definitions area.
;
; To confirm that the expression works properly, change x to 12 and y to 5,
; then click RUN. The result should be 13.
;
; Your mathematics teacher would say that you computed the distance formula. To
; use the formula on alternative inputs, you need to open DrRacket, edit the
; definitions of x and y so they represent the desired coordinates, and click
; RUN. But this way of reusing the distance formula is cumbersome and naive. We
; will soon show you a way to define functions, which makes reusing formulas
; straightforward. For now, we use this kind of exercise to call attention to
; the idea of functions and to prepare you for programming with them.
; ------------------------------------------------------------------------------

(define x 12)   ; (define x 3)
(define y 5)    ; (define y 4)

(sqrt (+ (sqr x) (sqr y)))
; => 13         ; => 5