DrRacket recursive definition - Week of November 12th

I never did have much time to think of a way to take the sum of the areas of the pyramid levels, not yet anyways.  I did figure out how to make drracket do it 'the long way' however.  I used the recursive definitions we learned in class to make racket take the sum of the bottom layer of a pyramid then work its way up. It was pretty straight forward and looked like this

(require picturing-programs)

(define (sum n) (/ (* n (+ n 1)) 2))

(define (vol n)

  (cond

    [(equal? n 1) 1]

    [else (+ (sum n) (vol (- n 1)))]))

It does feel a bit like cheating and I do still plan on trying to think of a single expression for the volume. It is neat to see so easily that the 'volume' of one of these pyramids with a bottom side of n=200 is 1,353,400 bottle caps. 

Theo