Number Theory and the Periodicity of Matter

(374 Seiten)
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Jan C. A. Boeyens
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"The main purpose of the book is to communicate a fundamental principle to the scientific world. The eventual impact of the subject matter is considered to be much wider than the readership of the preliminary accounts which have been published. The number principle at issue is known to be of wide general interest and the book has also been written to be accessible to nonspecialists. The potential readership should extend way beyond academic scientists.
Introduction Number Magic Periodic Structures Nuclear Synthesis Nuclidic Periodicity and Stability Hidden Symmetry Number Patterns Cosmic Structure Nuclear Structure and Properties Holistic Symmetry Number Theory Primer Introduction Numbers and Arithmetic Distribution of Prime Numbers Fibonacci Numbers Rational Fractions Modular Arithmetic Periodic Arithmetic Functions Periodic Table of the Elements Historical Development Theoretical Development Conclusion Structure of Atomic Nuclei Introduction Mass and Binding Energy Theoretical Models Particle Physics Elements of Cosmography Historical Cosmological Paradoxes Cosmological Models Chirality of Space-time The Vacuum Substratum The Periodic Laws Introduction Number Spiral and Periodic Laws General Periodic Function Hidden Symmetry Neutron Periodicity Nuclide Periodicity Periodicity and Number Theory Introduction Nuclear Synthesis by a-particle addition Nuclides in Farey Sequence Triangle of Stability Nuclear Stability Golden Parabola Properties of Atomic Matter Periodicity Nuclear Stability Nuclear Structure The Grand Pattern The Golden Ratio Nuclear Structure Five Domains Matter Transformation The Golden Excess Introduction Nuclide Periodicity Superfluidity Structure of the Nucleus Superconductivity Nuclear Stability Chemical Periodicity Introduction Electronegativity Chemical Bonding Epilogue
Of all the great innovations and intellectual achievements of mankind there is nothing that rivals the invention of counting and discovery of the number system. The way in which this discovery led to the development of abstract higher mathematics is the least of its merits, compared to the universal f- cination that the natural numbers hold for all people. Numbers are at the roots of magic, superstition, religion and science. Numerologists can int- pret great historical and cosmicevents, predict thefuture and explain human nature. Better informed, sophisticated people may frown upon and ridicule such claims,but the number of incidents that link numbers tophysical e?ects is simply too large to ignore as mere coincidence. It is in cases like these that the more respectable number theory is substituted for numerology. Although it is recognized as the most fundamental branch of mathem- ics,thevocabulary ofnumbertheoryincludesconcepts suchasprimenumber, perfect number, amicable number, square number, triangular number, py- midal number, and even magic number, none of which sounds too scienti?c and may suggest a di?erent status for the subject. Not surprisingly, number theory remains the pastime of amateurs and professionals alike – all the way from the great Gauss down. It may be claimed that abstract number theory is more lofty than mundane science, never to be degraded into a servant of physical theory.

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