A Probabilistic Proof of Wallis's Formula for π
نویسنده
چکیده
There are many beautiful formulas for π (see for example [4]). The purpose of this note is to introduce an alternate derivation of Wallis’s product formula, equation (1), which could be covered in a first course on probability, statistics, or number theory. We quickly review other famous formulas for π, recall some needed facts from probability, and then derive Wallis’s formula. We conclude by combining some of the other famous formulas with Wallis’s formula to derive an interesting expression for log(π/2) (equation (5)). Often in a first-year calculus course students encounter the Gregory-Leibniz formula, π
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 115 شماره
صفحات -
تاریخ انتشار 2008