TITLE:
A Construction That Produces Wallis-Type Formulas
AUTHORS:
Joshua M. Fitzhugh, David L. Farnsworth
KEYWORDS:
Wallis’s Formula; Unit p-Circle; Infinite Product; π; Gamma Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.6,
August
29,
2013
ABSTRACT: Generalizations of the geometric construction that repeatedly
attaches rectangles to a square, originally given by Myerson, are presented.
The initial square is replaced with a rectangle, and also the dimensionality of
the construction is increased. By selecting values for the various parameters,
such as the lengths of the sides of the original rectangle or rectangular box
in dimensions more than two and their relationships to the size of the attached
rectangles or rectangular boxes, some interesting formulas are found. Examples
are Wallis-type infinite-product formulas for the areas of p-circles with p > 1.