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Author: Ellen Kaplan Publisher: Bloomsbury Publishing USA ISBN: 1608192911 Category : Mathematics Languages : en Pages : 304
Book Description
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.
Author: Ellen Kaplan Publisher: Bloomsbury Publishing USA ISBN: 1608192911 Category : Mathematics Languages : en Pages : 304
Book Description
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.
Author: Andrea Barrett Publisher: Simon and Schuster ISBN: 0671731378 Category : Fiction Languages : en Pages : 260
Book Description
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.
Author: Ellen Kaplan Publisher: Bloomsbury Publishing USA ISBN: 1596915226 Category : Mathematics Languages : en Pages : 304
Book Description
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.
Author: JanetK. Halfyard Publisher: Routledge ISBN: 1351574205 Category : Music Languages : en Pages : 354
Book Description
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.
Author: Jay Todd Publisher: Wipf and Stock Publishers ISBN: 1498218830 Category : Religion Languages : en Pages : 145
Book Description
One of the major shifts in OT studies over the past half of a century has been the move away from studies dominated by diachronic matters toward more text-immanent, synchronic approaches. In Psalter studies, one can see such a shift on two levels. First, on the level of the individual psalm, there has been a general trend to focus on the literary and linguistic features as the proper means for discerning the meaning of the poem. Second, on the level of the Psalter as a whole, scholars have devoted significant attention to its canonical shape and the role of adjacent psalms in the interpretation of each individual psalm. In Remember, O Yahweh, Todd approaches Psalms 135--137 on both of these levels. After a detailed poetic analysis of each psalm, he proposes that Psalms 135--137 serve as a bridge between the Songs of Ascents (Pss 120--134) and the Last Davidic Psalter (Pss 138--145). As such, this group highlights Yahweh's past acts of deliverance as the basis for the post-exilic community's prayer for Yahweh to remember his people's lowly condition.
Author: Ian Aitken Publisher: Manchester University Press ISBN: 1526141744 Category : Performing Arts Languages : en Pages : 255
Book Description
‘Realist film theory and cinema’ embraces studies of cinematic realism and 19th century tradition, the realist film theories of Lukács, Grierson, Bazin and Kracauer, and the relationship of realist film theory to the general field of film theory and philosophy. This is the first book to attempt a rigorous and systematic application of realist film theory to the analysis of particular films. The book suggests new ways forward for a new series of studies in cinematic realism, and for a new form of film theory based on realism. It stresses the importance of the question of realism both in film studies and in contemporary life. Aitken’s work will be of interest to scholars and advanced students of film studies, literary studies, media studies, cultural studies and philosophy.
Author: Ellen Kaplan
Author: Ellen Kaplan
Author: André Romijn
Author: Andrea Barrett
Author: Evelyn Simms
Author: Ellen Kaplan
Author: JanetK. Halfyard
Author: Jay Todd
Author: Margaret Small
Author: Ian Aitken
Author: Library of Congress. Copyright Office