The Russian bio-physicist Sergei Petoukhov has shown that a family of bisymmetric 2n x 2n matrices encode the structure of the four DNA bases, the 64 codons that make up the 20 amino acids, and the proteins in all living structures. He discovered that the elements of the square roots of these matrices are all powers of the golden mean. We have generalized his matrices and shown that the square roots of general bisymmetric matrices are generalizations of the golden mean including a subclass that corresponds to the family of silver means. Powers of these matrices are also shown to generate all Pythagorean triples. We have also shown that tensor products of these matrices reproduce a table of successive musical fifths first recognized by the Syrian mathematician, Nicomachus, in 150 AD. The Nicomachus table also reveals the proportional system of the Parthenon that was the basis of the proportional system used for Renaissance architecture. The golden mean was developed into a modern system of proportions by the architect LeCorbusier, while the silver mean was the basis of the Roman system of architectural proportions. Pascal’s triangle also plays a role in the analysis. This talk will bring together many of these themes.

BIOGRAPHY

Jay Kappraff is an Associate Professor of Mathematics at NJIT. He is the author of two books, Connections: The Geometric Bridge between Art and Science and Beyond Measure: A Guided Tour through Nature, Myth, and Mathematics both published by World Scientific. He is the author of more than fifty papers on a variety of subjects from plasma physics, plant phyllotaxis, music and mathematics, and the relationship between mathematics, art, architecture and design. He is on the editorial board of the Japanese Journal FORMA and edited a special issue on the golden mean. He created eleven half-hour videotapes on Mathematics of Design that appeared on Cable TV of NJ numerous times and won a CAPE award for best distance learning course in science. He is the originator of an award winning pre-college course in Mathematics and Communications. He is the director of the NJIT Technology and Society Forum Series.

For information, contact either:
Ms. Brenda Walker at (973)596-3513 or at brenda.e.walker@njit.edu or
Dr. Andrew U. Meyer: at meyer@njit.edu.

Information and directions to NJIT are also available on the Web at http://www.njit.edu/University/Directions.html

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