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A Construction That Produces Wallis-Type Formulas
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA
- 1 School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA
- 2 School of Mathematical Sciences, Rochester Institute of Technology, Rochester, USA
Advances in Pure Mathematics·Volume 03 (2013)·Pages 579–585·Published 29 August 2013·DOI10.4236/apm.2013.36074
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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.
KeywordsWallis’s FormulaUnit p-CircleInfinite ProductπGamma Function
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