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.
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is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources.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.
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.
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.
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.”
An Intertextual Study on the New Exodus Pattern in the Theology of John
Author: Andrew C. Brunson
Publisher: Mohr Siebeck
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.
London has a unique series of churches built after the Great Fire of 1666, when most of the City of London was destroyed. Among these iconic churches are St Paul's, St Mary-le-Bow, St Bride's, St Clement Danes, St Martin-in-the-Fields, St Mary-le-Strand, St George Bloomsbury and Christ Church Spitalfields. They remain today as outstanding landmarks that define their local cityscapes. Designed by Sir Christopher Wren and his followers - Hawksmoor, Gibbs, Archer and James - these beautiful churches embody spiritual principles expressed through the conventions of Classical architecture. Underlying their outward, visible forms is sacred geometry, an ancient art that explores the invisible inner structure of the Cosmos and gives expression to it in physical form. In this book, Nigel Pennick explains the sacred geometry, spiritual symbols and emblems that make these churches among the most notable buildings of London.
This book traces the origins of a faith--perhaps the faith of the century. Modern revolutionaries are believers, no less committed and intense than were Christians or Muslims of an earlier era. What is new is the belief that a perfect secular order will emerge from forcible overthrow of traditional authority. This inherently implausible idea energized Europe in the nineteenth century, and became the most pronounced ideological export of the West to the rest of the world in the twentieth century. Billington is interested in revolutionaries--the innovative creators of a new tradition. His historical frame extends from the waning of the French Revolution in the late eighteenth century to the beginnings of the Russian Revolution in the early twentieth century. The theater was Europe of the industrial era; the main stage was the journalistic offices within great cities such as Paris, Berlin, London, and St. Petersburg. Billington claims with considerable evidence that revolutionary ideologies were shaped as much by the occultism and proto-romanticism of Germany as the critical rationalism of the French Enlightenment. The conversion of social theory to political practice was essentially the work of three Russian revolutions: in 1905, March 1917, and November 1917. Events in the outer rim of the European world brought discussions about revolution out of the school rooms and press rooms of Paris and Berlin into the halls of power. Despite his hard realism about the adverse practical consequences of revolutionary dogma, Billington appreciates the identity of its best sponsors, people who preached social justice transcending traditional national, ethnic, and gender boundaries. When this book originally appeared The New Republic hailed it as "remarkable, learned and lively," while The New Yorker noted that Billington "pays great attention to the lives and emotions of individuals and this makes his book absorbing." It is an invaluable work of history and contribution to our understanding of political life.
A memoir of spiritualism and self-discovery from the acclaimed, award-winning author At fifty, Alix Kates Shulman, author of the celebrated feminist novel, Memoirs of an Ex-Prom Queen, left a city life dense with political activism, family and literary community, and went to live alone on an island off the coast of Maine. On a windswept beach, in a cabin with no plumbing, power, or telephone, she found that she was learning to live all over again. In this luminous, spirited book, she charts her subsequent path as she learned not simply the joys of meditative solitude, but to integrate her new awareness into a busy, committed, even hectic mainland life. “A ten-year voyage of discovery . . . Shulman's honesty and sense of inquiry carry us with her all the way--could even, if we were willing, change our lives.” —San Francisco Sunday Examiner & Chronicle
Cristina Necula's poetry is an arpeggio of hidden harmonies vibrating at the finest touch. The personages traveling through the poet's life are instruments of self-knowledge; the means for the poet to rediscover deep echoes within her own psyche, for it is her emotional and psychological journey that takes center stage. Her poetry is full of substance and flavor, it surprises and enchants; it allows the reader's imagination to walk hand-in-hand with the poet's emotional states. The poems are full of the agony of illusion, which the poet considers at times beneficial - a surrogate for happiness - and in other instances, a treacherous guide which leads to self-deception. It is a paradox she uselessly tries to evade and destroy forever, but which continues to seduce her. Cristina Necula's poems are after all about the paradox of love in all its lure and mysterious grace. Sever Voinescu, writer
Francis Jenks,James Walker,Francis William Pitt Greenwood,William Ware
In this finely drawn portrait, Sappho of Lesbos narrates her extraordinary life, from her childhood in war-torn Mitylene to her later relentless search for passionate love. Driven by the all-consuming fever of her Muse-inspired poetic gift, Sappho leads the reader on a journey that is at once turbulent and divine, desperate and sensuous. With breathtaking lucidity and great leaps of imagination, Nancy Freedman shows us a Sappho we have never known -- and one we will never forget. The toast of kings for her verse, Sappho was also a shrewd businesswoman, an educator, an advocate of women's equality, and a rebel who was banished from her island home. Remembering her solely as a lesbian icon reveals only one aspect of her multifaceted personality. Here, finally, Nancy Freedman gives us the complete Sappho. She was arguably the most accomplished lyric poet of the ancient world, but her writing was all but destroyed by the early Church. Only in this century have fragments been uncovered, so that we too may glimpse the force of this strangely enigmatic woman. Contradictory in nature, she inspired equally passionate adoration and loathing; her fame brought her a series of obsessive loves. Her relations with women are well known, but it was for the love of a man that she set sail to face her destiny.