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LAPLACIAN EIGENSTRUCTURE OF THE EQUILATERAL TRIANGLE
      by Brian J. McCartin
"... The present book narrates this mathematical journey by providing a complete and self-contained treatment of the eigenstructure of the Laplacian on an equilateral triangle. The historical context and practical significance of the problem is carefully traced. The separate cases of Dirichlet, Neumann, radiation, absorbing and impedance boundary conditions are individually and exhaustively treated with the Dirichlet and Neumann cases also extended from the continuous to the discrete Laplacian. Corresponding results for the Sturm- Liouville boundary value problem under an impedance boundary condition are reviewed and applied to the parallel plate waveguide. Polygons with trigonometric eigenfunctions receive comprehensive study. Application to modal degeneracy in equilateral triangular waveguides has also been included."   Read more


MYSTERIES OF THE EQUILATERAL TRIANGLE
      by Brian J. McCartin
BOOK REVIEW by Philip J. Davis
Celebrating Equilateralism, SIAM News, Volume 45, Number 1, January/February 2012

"... Contributor of a substantial addition to the literature of triangle geometry, Brian J. McCartin of Kettering University, a prize-winning author, has fallen in love with the equilateral triangle. Even as mathematician Lewis Carroll had his Snark pursued with “forks and hope,” McCartin has pursued the equilateral triangle with a fine-tooth comb supported by an eagle eye. He has tracked down the multiple personality of the equilateral triangle as it appears in history, design; in theorems of plane geometry; in applications, games, recreational mathematics, competitions (e.g., the Olympiads); and in popular culture."   Read more


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