Kappraff, J.; Petoukhov, S. Symmetries, generalized numbers and harmonic laws in matrix genetics. (English) Zbl 1274.05053 Symmetry Cult. Sci. 20, No. 1-4, 23-49 (2009). Summary: This paper is devoted to the presentation and analysis of matrix representations of the genetic code. Principal attention is paid to a family of the genetic matrices which are constructed on the basis of Gray code ordering of their rows and columns. This Gray code ordering reveals new connections of the genetic code to: 8-dimensional bipolar algebras; Hadamard matrices; golden matrices; Pythagorean musical scale, and an integer triangle attributed to Nicomachus, a Syrian mathematician from the second century A.D. All of these mathematical entities possess symmetrical features. Some questions about silver means and Pythagorean triples are also described by these genetic matrices and their generalizations. MSC: 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) Keywords:genetic code; Gray code; multidimensional algebra; Hadamard matrices; golden section; Pythagorean musical scale; bisymmetric matrices; silver means; Pythagorean triples PDFBibTeX XMLCite \textit{J. Kappraff} and \textit{S. Petoukhov}, Symmetry Cult. Sci. 20, No. 1--4, 23--49 (2009; Zbl 1274.05053)