The following classical formulas for computing the value of were developed by Franois Vite (15401603) and Gottfried von Leibniz (16461716), respectively: and (a) Use

The following classical formulas for computing the value of π were developed by François Viète (1540–1603) and Gottfried von Leibniz (1646–1716), respectively:

and

(a) Use the product of the first three terms of Viète’s formula and the sum of the first four terms of Leibniz’s formula to approximate pi. Which formula is more accurate?

(b) Use the table function on a graphing calculator or a spreadsheet to determine how many terms of the second formula must be added together to produce the same accuracy as the product of the first three terms of the first formula.

= 2 V2 + 2 V2+V2 + 2 V2 V2