An Elementary Proof of the Wallis Product Formula for pi
نویسنده
چکیده
by repeated partial integration. The topic is usually reserved for more advanced calculus courses. The purpose of this note is to show that (1) can be derived using only the mathematics taught in elementary school, that is, basic algebra, the Pythagorean theorem, and the formula π · r 2 for the area of a circle of radius r . Viggo Brun gives an account of Wallis’s method in [1] (in Norwegian). Yaglom and Yaglom [2] give a beautiful proof of (1) which avoids integration but uses some quite sophisticated trigonometric identities.
منابع مشابه
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 114 شماره
صفحات -
تاریخ انتشار 2007