Felix Klein

Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree is a mathematical book written by Felix Klein. The book is divided into two parts. The first part of the book discusses the properties of the icosahedron, which is a three-dimensional geometric shape with 20 equilateral triangles as its faces. Klein explores the symmetry and geometry of the icosahedron and its relationship to other shapes in mathematics. The second part of the book focuses on the solution of equations of the fifth degree. This is a problem that had puzzled mathematicians for centuries, and Klein presents a comprehensive and detailed account of the various attempts to solve this problem. He also provides his own solution to the problem, which involves the use of the icosahedron. Overall, Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree is a seminal work in the field of mathematics. It is a must-read for anyone interested in geometry, algebra, or the history of mathematics. This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

The Theory of the Top: Volume III. Perturbations: Astronomical and Geophysical Applications is the third installment in a series of four self-contained English translations of the classic and definitive treatment of rigid body motion. Key features:* Complete and unabridged presentation with recent advances and additional notes;* Annotations by the translators provide insights into the nature of science and mathematics in the late 19th century;* Each volume interweaves theory and applicationsThe Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. Graduate students and researchers interested in theoretical and applied mechanics will find this series of books a thorough and insightful account. Other volumes in the series include the Introduction to the Kinematics and Kinetics of the Top, Development of a Theory of the Heavy Symmetric Top, and Technical Applications of the Theory of the Top.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Als Felix Klein den Plan faBte, die wichtigsten seiner autogra- phierten Vorlesungen im Druck erscheinen zu lassen, gedachte er, mit der Nichteuklidischen Geometrie zu beginnen und den alten Text zu- vor mit Hille eines jiingeren Geometers, des Herro Dr. Rosemann, in der Anlage und den Einzelheiten einer griindlichen Neubearbeitung zu unterziehen. Diese Arbeit erwies sich als langwieriger wie urspriing- lich geschatzt. Klein selbst konnte ihren AbschluB nicht mehr erleben. Zwar hatte er in taglichen, durch mehr als ein J ahr fortgesetzten Be- sprechungen den Stoff bis in die Einzelheiten hinein mit seinem Mit- arbeiter durchdacht, gesichtet und geordnet; aber die eigentliche Aus- arbeitung des Textes muBte er von vornherein Herro Rosemann uber- lassen. Bei Kleins Tode lagen die Fahnenkorrekturen der ersten Ka- pitel vor; es bedurfte jedoch noch jahrelanger opferwilliger Arbeit seitens Herro Rosemanns, urn auf Grund des urspriinglichen Programmes das Manuskript fertigzustellen und den Druck durchzufiihren. So ist bei diesem Werke eigener Antell und Verdienst, aber auch eigene Ver- antwortung des Bearbeiters viel heher zu bewerten als sonst ublich.

The Theory of the Top. Volume II. Development of the Theory in the Case of the Heavy Symmetric Top is the second in a series of four self-contained English translations of the classic and definitive treatment of rigid body motion. Key features: * Complete and unabridged presentation with recent advances and additional notes * Annotations by the translators provide insights into the nature of science and mathematics in the late 19th century * Each volume interweaves theory and applications The first volume established the general kinematic and kinetic foundations of the theory. Volume II discusses the motion of the symmetric top with a fixed support point, under the influence of gravity, in all its details. The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. Graduate students and researchers interested in theoretical and applied mechanics will find this a thorough and insightful account. Other works in this series include Volume I. Introduction to the Kinematics and Kinetics of the Top, Volume III. Perturbations. Astronomical and Geophysical Applications, and Volume IV. Technical Applications of the Theory of the Top.

TheTheory of the Top attained its great fame from both its monum- tal scope and its outstanding authors. In the early twentieth century, Felix Klein was known as a mathematician of world fame; Arnold S- merfeld, Klein’s disciple, had acquired his reputation as a rising star of theoretical physics. By 1910, when the ?nal volume of this tr- tise was published, the names of Klein and Sommerfeld would signal to a student that a matter as complex as the top was presented in a most authoritative manner, from the perspective of both mathem- ics and physics. The work also stands out in other regards: by its sheer extent—four volumes comprising a total of almost a thousand pages—and by the time lag of about ?fteen years between inception and completion. Klein himself regarded the ?nal result as somewhat disjointed. Its “idiosyncratic disposition,” he re?ected in 1922, may be understood only by taking into account the historic circumstances at its inception in 1895; the developments between the ?rst and last parts derailed the project from its intended course, so that for the technical applications described in Volume IV “almost no use was made of the theoretical framework developed atthebeginning”[Klein 1922, p. 659]. Itseemsappropriate,therefore,torecallthehistoricalcircumstances under which this treatise was conceived and pursued. Felix Klein was not only a renowned mathematician, but also an entrepreneurial and ambitious university professor striving for a broader acknowledgment of mathematics as a cultural asset.

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.