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Author: David S. Richeson
Publisher: Princeton University Press
ISBN: 0691218722
Category : Mathematics
Languages : en
Pages : 450
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Book Description
A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.
Author: David S. Richeson
Publisher: Princeton University Press
ISBN: 0691218722
Category : Mathematics
Languages : en
Pages : 450
Get Book Here
Book Description
A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.
Author: Eric Maskin
Publisher: Columbia University Press
ISBN: 0231153287
Category : Business & Economics
Languages : en
Pages : 164
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Book Description
Kenneth Arrow's pathbreaking Òimpossibility theoremÓ was a watershed in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, nondictatorship, and independence. In this book, Amartya Sen and Eric Maskin explore the implications of ArrowÕs theorem. Sen considers its ongoing utility, exploring the theoremÕs value and limitations in relation to recent research on social reasoning, while Maskin discusses how to design a voting rule that gets us closer to the idealÑgiven that achieving the ideal is impossible. The volume also contains a contextual introduction by social choice scholar Prasanta K. Pattanaik and commentaries from Joseph E. Stiglitz and Kenneth Arrow himself, as well as essays by Sen and Maskin outlining the mathematical proof and framework behind their assertions.
Author: Winnifred Fallers Sullivan
Publisher: Princeton University Press
ISBN: 0691180954
Category : Law
Languages : en
Pages : 330
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Book Description
The Constitution may guarantee it. But religious freedom in America is, in fact, impossible. So argues this timely and iconoclastic work by law and religion scholar Winnifred Sullivan. Sullivan uses as the backdrop for the book the trial of Warner vs. Boca Raton, a recent case concerning the laws that protect the free exercise of religion in America. The trial, for which the author served as an expert witness, concerned regulations banning certain memorials from a multiconfessional nondenominational cemetery in Boca Raton, Florida. The book portrays the unsuccessful struggle of Catholic, Protestant, and Jewish families in Boca Raton to preserve the practice of placing such religious artifacts as crosses and stars of David on the graves of the city-owned burial ground. Sullivan demonstrates how, during the course of the proceeding, citizens from all walks of life and religious backgrounds were harassed to define just what their religion is. She argues that their plight points up a shocking truth: religion cannot be coherently defined for the purposes of American law, because everyone has different definitions of what religion is. Indeed, while religious freedom as a political idea was arguably once a force for tolerance, it has now become a force for intolerance, she maintains. A clear-eyed look at the laws created to protect religious freedom, this vigorously argued book offers a new take on a right deemed by many to be necessary for a free democratic society. It will have broad appeal not only for religion scholars, but also for anyone interested in law and the Constitution. Featuring a new preface by the author, The Impossibility of Religious Freedom offers a new take on a right deemed by many to be necessary for a free democratic society.
Author: Nikk Effingham
Publisher:
ISBN: 0198842503
Category : Philosophy
Languages : en
Pages : 260
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Book Description
Time travel is metaphysically possible. Nikk Effingham contends that arguments for the impossibility of time travel are not sound. Focusing mainly on the Grandfather Paradox, Effingham explores the ramifications of taking this view, discusses issues in probability and decision theory, and considers the potential dangers of travelling in time.
Author: Ian Lynam
Publisher:
ISBN: 9789493148390
Category :
Languages : en
Pages : 212
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Book Description
The Impossibility of Silence' is a book for artists, designers and photographers interested in approaching writing about their vocation and culture. Drawing upon decades of experience as a writer, designer, artist and teacher, Ian Lynam offers up a plethora of inspirational and concrete approaches to writing about creative fields.
Author: Michael Slote
Publisher: OUP USA
ISBN: 0199790825
Category : Philosophy
Languages : en
Pages : 178
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Book Description
The book utilizes feminist thought and other philosophical considerations to argue in a unique way for an ethical picture of human life that stands in marked contrast with traditional understandings. Slote here revives Isaiah Berlin's bold views on the impossibility of perfection in ways that no one has previously attempted. The Appendix describes a new kind of philosophical/ethical methodology that combines and balances (traditionally) "feminine" and "masculine" elements.
Author: Mehran Kamrava
Publisher: Yale University Press
ISBN: 0300215622
Category : History
Languages : en
Pages : 312
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Book Description
Cover -- Contents -- Preface -- 1 Introduction -- 2 The Lessons of History -- 3 The Lay of the Land -- 4 One Nation, Divisible -- 5 The Travails of State-Building -- 6 The Road Ahead -- Notes -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z
Author: Zachary Storch
Publisher:
ISBN: 9780990999607
Category :
Languages : en
Pages :
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Book Description
Three million years ago, the planetary system of Za'nar's connection to the Magic-providing Void Plane was failing. To prevent the disappearance of Za'nar, a Magical Link between it and Earth was created. The Link shares much back and forth between the two systems, including their connection to the Void Plane.Now, one year after the War and the establishment of a parliamentary monarchy in Za'nar, Earth is in trouble. Sael Ageis, accomplished Magi of Za'nar, meets earthlings Klyde Vance and Fae, and together they find themselves drawn into a three million year old Magical conflict, unlocking secrets about the human race.
Author: Jonathan Goldberg
Publisher: Duke University Press
ISBN: 0822374048
Category : Literary Criticism
Languages : en
Pages : 193
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Book Description
Offering a new queer theorization of melodrama, Jonathan Goldberg explores the ways melodramatic film and literature provide an aesthetics of impossibility. Focused on the notion of what Douglas Sirk termed the "impossible situation" in melodrama, such as impasses in sexual relations that are not simply reflections of social taboo and prohibitions, Goldberg pursues films by Rainer Werner Fassbinder and Todd Haynes that respond to Sirk's prompt. His analysis hones in on melodrama's original definition--a form combining music and drama--as he explores the use of melodrama in Beethoven's opera Fidelio, films by Alfred Hitchcock, and fiction by Willa Cather and Patricia Highsmith, including her Ripley novels. Goldberg illuminates how music and sound provide queer ways to promote identifications that exceed the bounds of the identity categories meant to regulate social life. The interaction of musical, dramatic, and visual elements gives melodrama its indeterminacy, making it resistant to normative forms of value and a powerful tool for creating new potentials.
Author: Katy Upperman
Publisher: Swoon Reads
ISBN: 1250127998
Category : Juvenile Fiction
Languages : en
Pages : 318
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Book Description
Told in two voices Mati, a devout Muslim from Afghanistan, and Elise, a seventeen-year-old whose brother was killed there, try to keep their budding romance secret from their families.
