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.

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.

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.

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.

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

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.

The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon’s program of braid monodromy factorization. By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods. Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.

We bring into full light some excerpts on musical subjects which were until now scattered throughout the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in. This means that our multicultural history of the sciences necessarily also becomes a review of the various dominant languages used in the different historical contexts. In this volume, the history of the development of the sciences is told as it happened in real contexts, not in an alienated ideal world.