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GOLDEN RATIO --- GOLDEN RATIO

The divine proportion : a study in mathematical beauty.
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ISBN: 0486222543 9780486222547 Year: 1970 Publisher: New York (N.Y.) Dover

The golden section
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ISBN: 0883855348 Year: 2001 Publisher: Washington Mathematical Association of America


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The beauty of fractals
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ISBN: 0883859718 9780883859711 0883851865 9780883851869 Year: 2010 Publisher: Washington, D.C. Mathematical Association of America

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The Beauty of Fractals includes six essays related to fractals, with perspectives different enough to give you a taste of the breadth of the subject. Each essay is self-contained and expository. Moreover, each of the essays is intended to be accessible to a broad audience that includes college teachers, high school teachers, advanced undergraduate students, and others who wish to learn or teach about topics in fractals that are not regularly in textbooks on fractals.


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The golden ratio and Fibonacci numbers
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ISBN: 1281869953 9786611869953 9812386300 9789812386304 9781281869951 Year: 1997 Publisher: River Edge, NJ

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In this text, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. Fibonacci series and generalized Finobacci series and their relationship to the golden ratio are also presented.


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De ontstelling van Pythagoras : over de geschiedenis van de goddelijke proportie
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ISBN: 9039107548 Year: 1998 Publisher: Kampen Kok Agora


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Encounters with Euclid
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ISBN: 9780691219813 0691219818 Year: 2021 Publisher: Princeton, NJ

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A sweeping cultural history of one of the most influential mathematical books ever writtenEuclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its lasting influence today.In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the workshops of Restoration London to the Jesuit mission in China and the artisans' studios of medieval Baghdad. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space.Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its continuing role in the timeless search for order and reason in an unruly world.


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Current Techniques and Materials in Dentistry
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Year: 2022 Publisher: Basel MDPI - Multidisciplinary Digital Publishing Institute

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With advances in dental materials and their clinical applications, as well as innovations in computer technology, dental treatment is constantly evolving. In particular, adhesion technology to the tooth surface, implant treatments, and the application of CAD/CAM technology are very interesting topics for clinical dentists. As a bonding technique, the influence of the pre-etched area of the tooth surface on the adhesive strength can be reduced by the new application of a functional monomer. Additionally, the effect of an advanced adhesive system as a universal adhesive-derived primer, when compared with the two-step adhesive, is helpful for updating the applications of new materials. Dental implants are one of the most interesting dental treatments. PEEK (polyetheretherketone) has recently been reported as a further innovation in polymer implant materials, although it has not yet met the requirements to be a biomechanical requirement. In the placement of mini-screws used in orthodontic treatments, micro-cracks caused by overtorquing in thick and hard bone, and the consequent heat production, can reduce the success rate. Computer-aided design/computer-aided manufacturing (CAD/CAM) techniques are becoming increasingly popular. Since complete dentures can be produced using an additive (3D printing) or subtractive (milling) process, CAD/CAM techniques for denture fabrication have many clinical and laboratory advantages. Innovative and convenient dental material technology will be more and more expected in the future. This book has limited findings, but we hope that your clinical capability will be integrated and upgraded.

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