On Morley's theorem, determinantal identities and the QR algorithm

Three results are shown in this contribution. First, the diagram used in the proof of Morley's theorem is shown to provide a template for the creation of a closed solid figure. Second, it is shown how a proposition governing a class of determinants can be used to produce a rich supply of identities involving, e.g., Fibonacci and related families of numbers. Finally, it is shown in the case of an arbitrary 2 x 2 symmetric matrix A, how to obtain explicit expressions for all the elements of all the matrices involved in implementing the determination of the eigenvalues of A by means of the QR algorithm.