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 ...

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). ...

The m-clover is the plane curve defined by the polar equation rm/2 = cos (m2 θ). In this article we extend a well-known derivation of the Wallis product to derive a generalized Wallis product for arc lengths of m-clovers.

This equation becomes Wallis’ product when p = 0 and Vieta’s formula as p → ∞. It is surprising that such a connection between the two products was not discovered earlier. The collection [1] contains both original papers of Vieta and Wallis as well as other fundamental papers in the history of π. Indeed, there are many good historical sources on π. The text by P. Eymard and J. P. Lafon [6] is a...

Asthma is considered as one of the most common chronic diseases in the world. As a result of serious physical, social, and psychological complications, asthma can reduce health-related quality of life (HRQoL). The present study was designed to assess the HRQoL including physical health, general health perception, emotional health, psychological health, and social functioning of asthmatic patien...