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Hidden Harmonies

Author: Ellen Kaplan
Publisher: Bloomsbury Publishing USA
ISBN: 1608192911
Size: 47.28 MB
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A squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons-not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name. How can a theorem have more than one proof? Why does this one have more than two hundred-or is it four thousand? The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning-the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples. Like the authors' bestselling The Nothing That Is and Chances Are . . .-hailed as "erudite and witty," "magnificent," and "exhilarating"-Hidden Harmonies makes the excitement of mathematics palpable.

Hidden Harmony Geometric Fantasies

Author: Umberto Bottazzini
Publisher: Springer Science & Business Media
ISBN: 1461457254
Size: 63.66 MB
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​This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.​

Hearing Secret Harmonies

Author: Anthony Powell
Publisher: Random House
ISBN: 1409037916
Size: 76.81 MB
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The final novel in Anthony Powell's brilliant twelve-novel sequence, A Dance to the Music of Time. Discover the extraordinary life of Anthony Powell – captured by acclaimed biographer Hilary Spurling in Anthony Powell: Dancing to the Music of Time – available now in hardback and ebook from Hamish Hamilton.

Berio S Sequenzas

Author: Janet K. Halfyard
Publisher: Ashgate Publishing, Ltd.
ISBN: 9780754654452
Size: 25.16 MB
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The Sequenza series is one of the most remarkable achievements of the late twentieth century - a collection of virtuoso pieces that explores the capabilities of a solo instrument and its player, making extreme technical demands of the performer whilst developing the musical vocabulary of the instrument in compositions so assured and so distinctive that each piece both initiates and potentially exhausts the repertoire of a new genre. In this book contributors demonstrate the richness of this repertoire and the many levels on which Berio and these landmark compositions can be considered.

The 20 Minute Chords And Harmony Workout

Author: Stuart Isacoff
Publisher: Shacor, Inc.
ISBN: 9780943748412
Size: 52.33 MB
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This book will make keyboard harmony easier than ever to understand and to play. It's a complete step-by-step guide to keyboard chords and how they work. You'll find music and diagrams covering the basics, inversions, chord progressions and more, with fun-filled drills and superb, clear explanations to make chords easy to understand.

Marshall Mcluhan And Northrop Frye

Author: B.W. Powe
Publisher: University of Toronto Press
ISBN: 1442616164
Size: 72.33 MB
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Marshall McLuhan and Northrop Frye are two of Canada's central cultural figures, colleagues and rivals whose careers unfolded in curious harmony even as their intellectual engagement was antagonistic. Poet, novelist, essayist and philosopher B.W. Powe, who studied with both of these formidable and influential intellectuals, presents an exploration of their lives and work in Marshall McLuhan and Northrop Frye: Apocalypse and Alchemy. Powe considers the existence of a unique visionary tradition of Canadian humanism and argues that McLuhan and Frye represent fraught but complementary approaches to the study of literature and to the broader engagement with culture. Examining their eloquent but often acid responses to each other, Powe exposes the scholarly controversies and personal conflicts that erupted between them, and notably the great commonalities in their writing and biographies. Using interviews, letters, notebooks, and their published texts, Powe offers a new alchemy of their thought, in which he combines the philosophical hallmarks of McLuhan's “The medium is the message” and Frye's “the great code.”

Psalm 118 In The Gospel Of John

Author: Andrew C. Brunson
Publisher: Mohr Siebeck
ISBN: 9783161479908
Size: 70.17 MB
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Andrew Brunson examines the presence and function of Ps 118 in the Gospel of John, placing particular emphasis on its interpretation in a New Exodus context which has previously not been developed in the Fourth Gospel. Following a comprehensive survey of Ps 118's Jewish setting, its role in the festivals, and its use in the Synoptic Gospels, special attention is given to the quotations in the Entrance Narrative.The author argues that John portrays Jesus as bringing an end to Israel's state of continuing exile by fulfilling the role reserved to Yahweh in the New Exodus. This culminates in the Entrance to Jerusalem where Jesus embodies the return of Yahweh to reign among his people. A literary study of the coming-sent theme in John underscores the extent to which Jesus is identified ontologically and functionally with the Father. A previously unnoticed allusion to Ps 118 and Jubilees in John 8.56 is explored, and attention is paid to establishing the presence and developing the function of several neglected allusions to the psalm in 10:7-10; 10:24-25; and 11:41-42.