7. Summary

The chapter is about doing math with numbers.

Essential summary

• Basic arithmetic

(+ 5 3)
(/ 13 7) ; thirteen divided by seven
(* 11 2)
(- 9 1) ; nine minus one
(- 8)
(quotient 21912 7)
(remainder 21912 7)

• Maximum, minimum, absolute value

(max 0 -4) ; ==> 0
(min 255 300) ; ==> 255
(abs -10) ; ==> 10

• Exponents, square root, squaring:

(expt 1.01 95) ; 1.01 to the 95 power is about 2.57
(sqrt 9) ; square root of 9 is three
(sqr 1241) ; when you square 1241 you get 1540081

• Inexact answers, checking with tolerance

> (sqrt 5) ; about 2.236
#i2.23606797749979

The #i at the start of #i2.236... means that the number is an “inexact” decimal. You should never use check-expect with inexact numbers, because the inexact results can be different on different computers! Instead, use check-within.

(check-within (sqrt 5) 2.236 0.001)

• Special numbers: both pi is built in. Your tests should still pass if you use either the buit in value of pi or 3.1415.

> pi
#i3.141592653589793

• Getting rid of fractions. The best generic method to use is real->int. Otherwise there are specific functions that will round traditionally, round up (ceiling), and round down (floor).

(real->int 0.5)
(real->int 1.5)
(real->int 2.5)
(ceiling 1.2)
(floor 1.7)
(round 1.6)

More Important Ideas

• Inexact numbers and check-within
• build3-image or build-image
• map3-image or map-image
• (random 5) gives 0, 1, 2, 3, or 4.
• A remainder of zero means the numerator is a multiple of the denominator.
• How to make a gradient, changing color smoothly from pink to light blue.