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
Applied Mathematics, Kettering University, 1700 West Third Avenue, Flint 48504-4898, Michigan, USA
Copyright © 2002 Brian J. McCartin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.