Download or read book Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree written by Felix Klein and published by Courier Corporation. This book was released on 2003-01-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-known work covers the solution of quintics in terms of the rotations of a regular icosahedron around the axes of its symmetry. Its two-part presentation begins with discussions of the theory of the icosahedron itself; regular solids and theory of groups; introductions of (x + iy); a statement and examination of the fundamental problem, with a view of its algebraic character; and general theorems and a survey of the subject. The second part explores the theory of equations of the fifth degree and their historical development; introduces geometrical material; and covers canonical equations of the fifth degree, the problem of A's and Jacobian equations of the sixth degree, and the general equation of the fifth degree. Second revised edition with additional corrections.
Download or read book Lectures on the Icosahedron and the Solution of the Fifth Degree written by Felix Klein and published by Cosimo, Inc.. This book was released on 2007-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this classic of mathematical literature, first published in 1884, Felix Klein elegantly demonstrates how the rotation of icosahedron can be used to solve complex quintic equations. Divided into two parts-"Theory of the Icosahedron" and "The Theory of Equations of the Fifth Degree"-The Icosahedron covers: . the regular solids and the theory of groups . introduction of (x + iy) . statement and discussion of the fundamental problem, according to the theory of functions . the algebraical character of the fundamental problem . general theorems and survey of the subject . the historical development of the theory of equations of the fifth degree . introduction of geometrical material . the canonical equations of the fifth degree . the problem of the A's and the Jacobian equations of the sixth degree . the general equation of the fifth degree Complete with detailed equations and instructive material, The Icosahedron will be valued by experts in higher mathematics and students of algebra alike. German mathematician FELIX KLEIN (1849-1925) specialized in function theory, group theory, and non-Euclidean geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis; Elementary Mathematics from an Advanced Standpoint: Geometry; and Famous Problems of Elementary Geometry.
Download or read book Cremona Groups and the Icosahedron written by Ivan Cheltsov and published by CRC Press. This book was released on 2015-08-21 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and gives a proof of its A5-birational rigidity.The a
Download or read book The Jahn Teller Effect in C60 and Other Icosahedral Complexes written by C. C. Chancey and published by Princeton University Press. This book was released on 2021-02-09 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of the high symmetry involved, the Jahn-Teller effect is the natural starting point for considering electron-phonon (or vibronic) interactions in icosahedral molecules. This work is the first comprehensive theoretical analysis of the Jahn-Teller interaction in C60 and other icosahedral complexes. The importance of this research derives in part from the increasing, widespread interest in C60 and other molecular clusters and their application in science and industry. The electrical and spectroscopic properties of fullerene and fulleride compounds depend intimately on the coupling between the electronic and vibrational modes of these systems, and this book addresses the fundamental theoretical questions. In particular, a chapter is devoted to the connection between the theory and experimental observations, such as ESR (electron spin resonance) effects and molecular spectra. Earlier books have discussed the theory of Jahn-Teller interactions in lower symmetry structures (cubic, tetrahedral, tetragonal, trigonal,...); this is the first that focuses on the new icosahedral systems, whose most famous example is Buckminsterfullerene, C60. The book's authors have over fifty years of combined research experience into the theoretical aspects of the Jahn-Teller effect.
Download or read book The Fifty Nine Icosahedra written by H. S. M. Coxeter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation.
Download or read book Lectures on the Ikosahedron and the Solution of Equations of the Fifth Degree written by Felix Klein and published by . This book was released on 1888 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cut and Assemble Icosahedra written by Eve Torrence and published by Courier Corporation. This book was released on 2011-12-08 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fun, yet challenging shapes for hobbyists and useful tools for teachers of high school and college geometry, these 12 cut-and-assemble models offer complete step-by-step instructions and diagrams for assembly. Includes pre-colored pieces, plus blank color-your-own options.
Download or read book Extended Icosahedral Structures written by Marko V. Jaric and published by Elsevier. This book was released on 2012-12-02 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extended Icosahedral Structures discusses the concepts about crystal structures with extended icosahedral symmetry. This book is organized into six chapters that focus on actual modeling of extended icosahedral crystal structures. This text first presents a tiling approach to the modeling of icosahedral quasiperiodic crystals. It then describes the models for icosahedral alloys based on random connections between icosahedral units, with particular emphasis on diffraction properties. Other chapters examine the glassy structures with only icosahedral orientational order and the extent of translational order in such structures relates to the nature of their growth. Lastly, the use of the polytope concept to rationalize and construct real structures with varying degrees of icosahedral order is addressed. This book is of great value to physicists, crystallographers, metallurgists, and beginners in the field of quasicrystals.
Download or read book Polyhedra written by Anthony Pugh and published by Univ of California Press. This book was released on 1976 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Fifty Nine Icosahedra written by H. S. M. Coxeter and published by Springer. This book was released on 2013-03-26 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation.
Download or read book The Encyclop dia Britannica written by Hugh Chisholm and published by . This book was released on 1911 with total page 1066 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Viral Molecular Machines written by Michael G. Rossmann and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will contain a series of solicited chapters that concern with the molecular machines required by viruses to perform various essential functions of virus life cycle. The first three chapters (Introduction, Molecular Machines and Virus Architecture) introduce the reader to the best known molecular machines and to the structure of viruses. The remainder of the book will examine in detail various stages of the viral life cycle. Beginning with the viral entry into a host cell, the book takes the reader through replication of the genome, synthesis and assembly of viral structural components, genome packaging and maturation into an infectious virion. Each chapter will describe the components of the respective machine in molecular or atomic detail, genetic and biochemical analyses, and mechanism. Topics are carefully selected so that the reader is exposed to systems where there is a substantial infusion of new knowledge in recent years, which greatly elevated the fundamental mechanistic understanding of the respective molecular machine. The authors will be encouraged to simplify the detailed knowledge to basic concepts, include provocative new ideas, as well as design colorful graphics, thus making the cutting-edge information accessible to broad audience.
Download or read book The Physics and Chemistry of Carbides Nitrides and Borides written by R. Freer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carbides, nitrides and borides are families of related refractory materials. Traditionally they have been employed in applications associated with engineering ceramics where either high temperature strength or stability is of primary importance. In recent years there has been a growing awareness of the interesting electrical, thermal and optical properties exhibited by these materials, and the fact that many can be prepared as monolithic ceramics, single crystals and thin films. In practical terms carbides, nitrides and borides offer the prospect of a new generation of semiconductor materials, for example, which can function at very high temperatures in severe environmental conditions. However, as yet, we have only a limited understanding of the detailed physics and chemistry of the materials and how the preparation techniques influence the properties. Under the auspices of the NATO Science Committee an Advanced Research Workshop (ARW) was held on the Physics and Chemistry of Carbides, Nitrides and Borides (University of Manchester, 18-22 September, 1989) in order to assess progress to date and identify the most promising themes and materials for future research. An international group of 38 scientists considered developments in 5 main areas: The preparation of powders, monolithic ceramics, single crystals and thin films; Phase transformations, microstructure, defect structure and mass transport; Materials stability; Theoretical studies; Electrical, thermal and optical properties of bulk materials and thin films.
Download or read book The Mathematics of Harmony written by Alekse? Petrovich Stakhov and published by World Scientific. This book was released on 2009 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the ?Mathematics of Harmony,? a new interdisciplinary direction of modern science. This direction has its origins in ?The Elements? of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the ?golden? algebraic equations, the generalized Binet formulas, Fibonacci and ?golden? matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and ?golden? matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Download or read book Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry written by R. Bruce King and published by CRC Press. This book was released on 1992-12-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry is a text-reference that provides inorganic chemists with a rudimentary knowledge of topology, graph theory, and related mathematical disciplines. The book emphasizes the application of these topics to metal clusters and coordination compounds. The book's initial chapters present background information in topology, graph theory, and group theory, explaining how these topics relate to the properties of atomic orbitals and are applied to coordination polyhedra. Subsequent chapters apply these ideas to the structure and chemical bonding in diverse types of inorganic compounds, including boron cages, metal clusters, solid state materials, metal oxide derivatives, superconductors, icosahedral phases, and carbon cages (fullerenes). The book's final chapter introduces the application of topology and graph theory for studying the dynamics of rearrangements in coordination and cluster polyhedra.
Download or read book From Thales to Euclid written by Sir Thomas Little Heath and published by . This book was released on 1921 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A History of Greek Mathematics written by Sir Thomas Little Heath and published by . This book was released on 1921 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
