22a. Recursion Practice 3

Do at least the first three. Please make sure to write at least three tests for each function.

1. is-in-word?: string(letter) string(word) -> boolean. True if the letter is in the word, false otherwise.

   (check-expect (is-in-word? "x" "explode") true)
   (check-expect (is-in-word? "s" "juliuc caecar" false)

2. word-shrink: string(word) number(starting-size) -> image. Create a picture of the word in which each letter is four points smaller than the previous letter. Do not let the font size go below 5pt.

   

3. sum-penta: number(start) number(end) -> number. The pentagonal numbers are created by making larger and larger pentagons - Wikipedia has a nice animated image. The formula for the nth pentagonal number is (* 0.5 n (- (* 3 n) 1)).

   Find the sum of all of pentagonal number n from n=start through n=end.

   n	(penta n)	(sum-penta 1 n)
   1	1	1
   2	5	6
   3	12	18

Challenge

1. draw-tic-tac-toe: string -> image. Take a string containing 9 characters (from “X” “O” and “-”) and turn it into a 3x3 image of “X” “O” and blank squares in a tic-tac-toe board.

   Hint: You will probably want helper functions draw-one-space and draw-one-line.

   

2. (Math) Write is-pentagonal?: number -> boolean. Then read Project Euler 44, which might be doable soon. You can celebrate if you find any two pentagonal numbers whose sum and difference are both pentagonal.