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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.
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.
"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.
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.
""Hidden History Revealed"" offers a captivating exploration of overlooked events, forgotten innovators, and unsung heroes that have silently shaped our world. This groundbreaking book challenges readers to reconsider their understanding of historical cause and effect by delving into the shadows of the past. Through three main sections—""Unsung Heroes,"" ""Pivotal Moments in the Shadows,"" and ""Cross-Cultural Catalysts""—the author uncovers hidden historical elements that provide a more nuanced and comprehensive view of human civilization. What sets this book apart is its innovative approach to historical analysis, combining traditional historiography with big data analytics and network theory. By drawing upon recently declassified documents, oral histories from marginalized communities, and cutting-edge archaeological findings, the author presents a fresh perspective on world history. The book challenges Eurocentric views and offers a more balanced, inclusive narrative that spans cultures and regions throughout time. ""Hidden History Revealed"" balances academic rigor with accessibility, making it valuable for history enthusiasts, students, educators, and policymakers alike. By illuminating the hidden forces that have profoundly influenced our world, this book not only transforms our understanding of the past but also offers insights into addressing contemporary global challenges and fostering a more inclusive worldview.
This encyclopedic guide explores the rich and varied meanings of more than 2,000 symbols?from amethyst to Zodiac.