A Wallis Product on Clovers

2014/02/26 by Trevor Hyde · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Arithmetic #Geometry #Mathematics #Mathematics and Applications #Mathematics education #Product (mathematics) #Pure mathematics

paper · doi:10.4169/amer.math.monthly.121.03.237

published in American Mathematical Monthly 121(3), 237-243 (Taylor & Francis)

openalex publication_date 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The m-clover is the plane curve defined by the polar equation . 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.

Citations

• The lemniscate constants
• Geometry and Number Theory on Clovers

Cited by

• Generalizations of the Squircle-Lemniscate Relation and Keplerian Dynamics
• Lemniscate constant [wikipedia]
• Lemniscate elliptic functions [wikipedia]

Related

• A Wallis Product on Clovers
• Generalizing Wallis formula
• Generalising the Wallis Product
• The Helix Relation Between Two Curves
• New special curves and their spherical indicatrices