Mathematical Problems in Engineering 
Volume 8 (2002), Issue 6, Pages 517-539
doi:10.1080/1024123021000053664

Eigenstructure of the equilateral triangle, Part II: The Neumann problem

Brian J. McCartin

 Applied Mathematics, Kettering University, 1700 West Third Avenue, Flint 48504-4898, Michigan, USA

Abstract

Lame's formulas for the eigenvalues and eigenfunctions of the Laplacian with Neumann boundary conditions on an equilateral triangle are derived using direct elementary mathematical techniques. They are shown to form a complete orthonormal system. Various properties of the spectrum and nodal lines are explored. Implications for related geometries are considered.