Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
We prove some new upper and lower bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. In particular, we improve Pólya and Szegö's [ (1951)] lower bound for quadrilaterals and extend Hersch's [ (1966) 457–460] upper bound for parallelograms to general quadrilaterals.