Problem 1.12 (page 42). To be precise, let us define the function p for "Pascal" which takes two arguments:

 r -- the row number e -- the element number in the row 

So (p r e) is the value of element e in row r. And we number the rows starting from 0, and we also number the elements in each row starting from 0. (That is the usual convention.) Thus for instance,

 (p 0 0) evaluates to 1 (p 2 1) evaluates to 2 (p 4 2) evaluates to 6 

and so on. The problem then is to write a recursive Scheme procedure for the function p. And I really mean "recursive". For this problem, forget everything you ever learned about formulas for the elements of Pascal's triangle that involve factorials.

And I shouldn't really have to say this, but you should make sure you test your function, and indicate to me how you did this.

the following pattern of numbers is called Pascals triangle.

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

. . .

the numbers at the edge of the triangle are all 1, and each

number inside the triangle is the sum of the two numbers

above it.35 Write a procedure that computes elements of

Pascals triangle by means of a recursive process.