* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Full text
Survey
Document related concepts
Law of large numbers wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Infinitesimal wikipedia , lookup
History of mathematics wikipedia , lookup
Ethnomathematics wikipedia , lookup
List of important publications in mathematics wikipedia , lookup
History of logarithms wikipedia , lookup
Real number wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Non-standard analysis wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Large numbers wikipedia , lookup
Transcript
662 [Continued from page 660. ] Dec. 1972 puzzling phenomenon: nuclei having certain values for their N o r Z numbers a r e considerably more stable than others* These values a r e 2, 8, 14, 20, 28, 50, 82, and 126. These numbers were called "magic n u m b e r s , " since their origin was a mystery. Let us divide the magic numbers by 10 and express the results to the n e a r e s t integers. X X/10 Nearest Integer 2 8 0.2 0.8 14 1.4 20 2 28 2.8 50 5 82 8.2 126 12.6 0 1 1 2 3 5 8 13 We get the Fibonacci numbers from 0 to 13 • • • S We saw that the shell structure of the atom showed that the atomic numbers of stable atoms should be related to the Fibonacci s e r i e s . The phenomenon of the magic numbers thus indicates that the nucleus also might have a shell structure. The first successful model of the nucleus, the shell model, was put forward by Maria Goeppert Mayer, Hans Jensen, and Eugene Wigner. Calculations based on the shell model successfully explained the phenome- non of magic numbers. Thus the Fibonacci numbers seem to be associated with the stability of systems in dynamic equilibrium. Perhaps the Fibonacci sequence might help solve a number of problems in Physics. MOW A^AlJaABlLEJff COMBINATORIAL IDENTITIES A STANDARDIZED SET OF TABLES LISTING 500 BINOMIAL COEFFICIENT SUMMATIONS by Henry W. Gould, Professor of Mathematics, West Virginia University A corrected, revised, augmented edition of the legendary tables of 500 combinatorial identities originally circulated on a very limited basis in 1960. This edition actually con- tains several dozen new formulas, and all known e r r o r s in the first edition have been c o r rected. 116 pp. 22 x 28 cm. bound. 1972. Because of the enthusiastic reception accorded the original tables, and due to the continued demand for copies of these useful tables, the present edition has been produced to fill the need for these handy tables. The tables are analogous to a standard table of integrals. Sums of ratios of products of binomial coefficients of all kind are included, from the simplest form of the Vandermonde Convolution to DougalPs famous formula involving six coefficients divided by five. The tables a r e of value to .mathematicians in many fields: combinatorics, number theory, graph theory, special functions, statistics, probability, matrix theory, plied mathematics, computer science, etc. Copies may be secured at $10.00 each, postpaid, directly from: Henry W. Gould 1239 College Avenue Morgantown, W. Va. ORDER YOUR COPY TODAY!!! 26505 HAVE YOUR LIBRARY ORDER A COPY TODAY!!! ap-