Hidden Harmonies

Hidden Harmonies

Author: Ellen Kaplan

Publisher: Bloomsbury Publishing USA

Published: 2011-01-11

Total Pages: 304

ISBN-13: 1608192911

DOWNLOAD EBOOK

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.


Secret Harmonies

Secret Harmonies

Author: Andrea Barrett

Publisher: Simon and Schuster

Published: 1991-03

Total Pages: 260

ISBN-13: 0671731378

DOWNLOAD EBOOK

When childhood sweethearts Reba Dwyer and Luke Wyatt marry, they expect no surprises. But now that Luke is her husband, discord enters their lives. Secret Harmonies is utterly absorbing, moving story of what happens to this couple.


Hidden Harmonies

Hidden Harmonies

Author: Ellen Kaplan

Publisher: Bloomsbury Publishing USA

Published: 2011-01-04

Total Pages: 304

ISBN-13: 1596915226

DOWNLOAD EBOOK

The Harvard mathematician authors of The Art of the Infinite present a history of the famous relation "A squared plus B squared equals C squared" that assesses its contributors from da Vinci to the Freemasons while analyzing its numerous proofs and applications.


The Secret Life: Being the Book of a Heretic

The Secret Life: Being the Book of a Heretic

Author: Elizabeth Bisland

Publisher: Good Press

Published: 2019-12-05

Total Pages: 173

ISBN-13:

DOWNLOAD EBOOK

"The Secret Life: Being the Book of a Heretic" by Elizabeth Bisland Elizabeth Bisland Wetmore was an American journalist. This book served as a sort of journal of hers, where she discussed numerous topics and opinions. L'Enfant Terrible, An Optimistic Cynic, A Poet Sheep-rancher, An Eaten Cake, Concerning Elbows on the Table, and An Autumn Impulse are just some of the titled entries in this fascinating look at Bisland's mind.


Berio's Sequenzas

Berio's Sequenzas

Author: JanetK. Halfyard

Publisher: Routledge

Published: 2017-07-05

Total Pages: 328

ISBN-13: 1351574205

DOWNLOAD EBOOK

Between 1958 and 2002, Luciano Berio wrote fourteen pieces entitled Sequenza, along with several versions of the same work for different instruments, revisions of the original pieces and also the parallel Chemins series, where one of the Sequenzas is used as the basis for a new composition on a larger scale. 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. The Sequenzas have significantly influenced the development of composition for solo instruments and voice, and there is no comparable series of works in the output of any other composer. Series of pieces tend to be linked by the instruments for which the composer writes, but this is a series in which the pieces are linked instead by the variety of instruments for which Berio composed. The varied approaches taken by the contributors in discussing the pieces demonstrate the richness of this repertoire and the many levels on which Berio and these landmark compositions can be considered. Contributions are arranged under three main headings: Performance Issues; Berio's Compositional Process and Aesthetics; and Analytical Approaches.


Symbolism

Symbolism

Author: Robert Goldwater

Publisher: Routledge

Published: 2018-02-02

Total Pages: 280

ISBN-13: 042997664X

DOWNLOAD EBOOK

This encyclopedic guide explores the rich and varied meanings of more than 2,000 symbols?from amethyst to Zodiac.


The Writer's Way in France

The Writer's Way in France

Author: Robert Greer Cohn

Publisher: University of Pennsylvania Press

Published: 2016-11-11

Total Pages: 448

ISBN-13: 1512801321

DOWNLOAD EBOOK

This book is an attempt to present a new, integral approach to French literature. Acknowledging his debts to numerous post-Hegelian philosophers or psychologists and modern critics, Professor Cohn offers a lucid and swift-paced account of an original view of literature which bears particular kinship to the artistic visions of Joyce, Mallarmé, and Proust. In Part I the creative temperament is defined in terms of a subtly recognizable rhythm of human nature which appears in varying forms or "syncopations." In Part II the evolution of the rhythm is followed through changing themes, images, styles, and genres from the earliest known native origins to the crowning work of the Symbolists. Parts I and II together constitute a method, the purpose of which is to maintain, as tactfully as possible, a sense of direction as we move through the complexities of lively art. The method is brought to bear on extensive texts in Part III, with closely detailed studies of Rimbaud and Proust. These individual studies are offered' as examples; more are promised in subsequent volumes. In addition, the present state of criticism is discussed in an Introduction; lengthy appendices are devoted to some important modes of lyric poetry and the author's "precritical," or epistemological, concepts; and a briefer appendix takes up the idea of Progress in Art. The Writer's Way in France is a work of unusual perception, of great importance to all students of literature who are interested in fresh ideas and methods.