Compute Pi by Wallis Formula

• John Wallis (1616-1703) derived the following infinite sum expansion:

(2 * 2) * (4 * 4) * (6 * 6) * . . .

? / 2 = --------------------------------------

(1 * 3) * (3 * 5) * (5 * 7) * . . .

• Terms in Numerator

evens .^ 2

• Terms in Denominator

1 3 5 7 9 . . . odds

3 5 7 9 11 . . . odds + 2

------------------------

1*3 3*5 5*7 7*9 9*11 . . .

i.e., odds .* (odds + 2)

• Quotient

prod( (evens .^ 2) ./ (odds .* (odds+2)) )

• Successive approximations to Pi

pi = 2 .* cumprod( (evens.^2) ./ (odds .* (odds+2)) )

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