83:T5d3,Individual decision making can often be wrong due to misinformation, impulses, or biases. Collective decision making, on the other hand, can be surprisingly accurate. In Democratic Reason, Helene Landemore demonstrates that the very factors behind the superiority of collective decision making add up to a strong case for democracy. She shows that the processes and procedures of democratic decision making form a cognitive system that ensures that decisions taken by the many are more likely to be right than decisions taken by the few. Democracy as a form of government is therefore valuable not only because it is legitimate and just, but also because it is smart. Landemore considers how the argument plays out with respect to two main mechanisms of democratic politics: inclusive deliberation and majority rule. In deliberative settings, the truth-tracking properties of deliberation are enhanced more by inclusiveness than by individual competence. Landemore explores this idea in the contexts of representative democracy and the selection of representatives. She also discusses several models for the "wisdom of crowds" channeled by majority rule, examining the trade-offs between inclusiveness and individual competence in voting. When inclusive deliberation and majority rule are combined, they beat less inclusive methods, in which one person or a small group decide. Democratic Reason thus establishes the superiority of democracy as a way of making decisions for the common good.84:T528,

How digital networks are transforming art and architecture

Art as we know it is dramatically changing, but popular and critical responses lag behind. In this trenchant illustrated essay, David Joselit describes how art and architecture are being transformed in the age of Google. Under the dual pressures of digital technology, which allows images to be reformatted and disseminated effortlessly, and the exponential acceleration of cultural exchange enabled by globalization, artists and architects are emphasizing networks as never before. Some of the most interesting contemporary work in both fields is now based on visualizing patterns of dissemination after objects and structures are produced, and after they enter into, and even establish, diverse networks. Behaving like human search engines, artists and architects sort, capture, and reformat existing content. Works of art crystallize out of populations of images, and buildings emerge out of the dynamics of the circulation patterns they will house.

Examining the work of architectural firms such as OMA, Reiser + Umemoto, and Foreign Office, as well as the art of Matthew Barney, Ai Weiwei, Sherrie Levine, and many others, After Art provides a compelling and original theory of art and architecture in the age of global networks.

85:T641,

This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom.

The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.

86:T52d,We can see a theft, hear a lie, and feel a stabbing. These are morally important perceptions. But are they also moral perceptions--distinctively moral responses? In this book, Robert Audi develops an original account of moral perceptions, shows how they figure in human experience, and argues that they provide moral knowledge. He offers a theory of perception as an informative representational relation to objects and events. He describes the experiential elements in perception, illustrates moral perception in relation to everyday observations, and explains how moral perception justifies moral judgments and contributes to objectivity in ethics. Moral perception does not occur in isolation. Intuition and emotion may facilitate it, influence it, and be elicited by it. Audi explores the nature and variety of intuitions and their relation to both moral perception and emotion, providing the broadest and most refined statement to date of his widely discussed intuitionist view in ethics. He also distinguishes several kinds of moral disagreement and assesses the challenge it poses for ethical objectivism.
Philosophically argued but interdisciplinary in scope and interest, Moral Perception advances our understanding of central problems in ethics, moral psychology, epistemology, and the theory of the emotions.87:T6e2,The recent economic rise of China and India has attracted a great deal of attention - and justifiably so. Together, the two countries account for one-fifth of the global economy and are projected to represent a full third of the world's income by 2025. Yet, many of the views regarding China and India's market reforms and high growth have been tendentious, exaggerated, or oversimplified. "Awakening Giants, Feet of Clay" scrutinizes the phenomenal rise of both nations, and demolishes the myths that have accumulated around the economic achievements of these two giants in the last quarter century. Exploring the challenges that both countries must overcome to become true leaders in the international economy, Pranab Bardhan looks beyond short-run macroeconomic issues to examine and compare China and India's major policy changes, political and economic structures, and current general performance. Bardhan investigates the two countries' economic reforms, each nation's pattern and composition of growth, and the problems afflicting their agricultural, industrial, infrastructural, and financial sectors.He considers how these factors affect China and India's poverty, inequality, and environment, how political factors shape each country's pattern of burgeoning capitalism, and how significant poverty reduction in both countries is mainly due to domestic factors - not global integration, as most would believe. He shows how authoritarianism has distorted Chinese development while democratic governance in India has been marred by severe accountability failures. Full of valuable insights, "Awakening Giants, Feet of Clay" provides a nuanced picture of China and India's complex political economy at a time of startling global reconfiguration and change.88:T761,

The case for a thoughtful secularism from some of today's most distinguished scientists, philosophers, and writers

Can secularism offer us moral, aesthetic, and spiritual satisfaction? Or does the secular view simply affirm a dog-eat-dog universe? At a time when the issues of religion, evolution, atheism, fundamentalism, Darwin, and science fill headlines and invoke controversy, The Joy of Secularism provides a balanced and thoughtful approach for understanding an enlightened, sympathetic, and relevant secularism for our lives today. Bringing together distinguished historians, philosophers, scientists, and writers, this book shows that secularism is not a mere denial of religion. Rather, this positive and necessary condition presents a vision of a natural and difficult world—without miracles or supernatural interventions—that is far richer and more satisfying than the religious one beyond.

From various perspectives—philosophy, evolutionary biology, primate study, Darwinian thinking, poetry, and even bird-watching—the essays in this collection examine the wealth of possibilities that secularism offers for achieving a condition of fullness. Factoring in historical contexts, and ethical and emotional challenges, the contributors make an honest and heartfelt yet rigorous case for the secular view by focusing attention on aspects of ordinary life normally associated with religion, such as the desire for meaning, justice, spirituality, and wonder. Demonstrating that a world of secular enchantment is a place worth living in, The Joy of Secularism takes a new and liberating look at a valuable and complex subject.

The contributors are William Connolly, Paolo Costa, Frans de Waal, Philip Kitcher, George Levine, Adam Phillips, Robert Richards, Bruce Robbins, Rebecca Stott, Charles Taylor, and David Sloan Wilson.

89:T69a,In the year 1000, the economy of the Middle East was at least as advanced as that of Europe. But by 1800, the region had fallen dramatically behind--in living standards, technology, and economic institutions. In short, the Middle East had failed to modernize economically as the West surged ahead. What caused this long divergence? And why does the Middle East remain drastically underdeveloped compared to the West? In The Long Divergence, one of the world's leading experts on Islamic economic institutions and the economy of the Middle East provides a new answer to these long-debated questions. Timur Kuran argues that what slowed the economic development of the Middle East was not colonialism or geography, still less Muslim attitudes or some incompatibility between Islam and capitalism. Rather, starting around the tenth century, Islamic legal institutions, which had benefitted the Middle Eastern economy in the early centuries of Islam, began to act as a drag on development by slowing or blocking the emergence of central features of modern economic life--including private capital accumulation, corporations, large-scale production, and impersonal exchange. By the nineteenth century, modern economic institutions began to be transplanted to the Middle East, but its economy has not caught up. And there is no quick fix today. Low trust, rampant corruption, and weak civil societies--all characteristic of the region's economies today and all legacies of its economic history--will take generations to overcome. The Long Divergence opens up a frank and honest debate on a crucial issue that even some of the most ardent secularists in the Muslim world have hesitated to discuss.8a:T59d,One of the greatest attractions of a trip to Kenya is the chance to see animals such as lions, cheetah, leopards, zebra, and giraffe up close and in their natural habitats. "Animals of the Masai Mara" is a lavish photographic guide that explores the charismatic wildlife most likely to be encountered by a safari visitor to the Masai Mara National Reserve in southwest Kenya. More than 140 stunning photographs showcase 65 mammals and 17 reptile species, including 6 snakes. Designed to be informative and locally accurate, rather than purely identification-based, this easy-to-use book pays particular attention to wildlife behavior and is written from the firsthand experiences of the authors and the knowledge of local safari guides. Numerous "Top Tips" throughout show readers how and where to locate specific species. The only field guide to focus solely on the wildlife of the Masai Mara National Reserve, "Animals of the Masai Mara" will be indispensable to visitors to this famous park and all nature enthusiasts with an interest in this area of the world. This is the only photographic guide specific to the animals of the Masai Mara National Reserve.It includes more than 140 remarkable photographs covering 65 mammals and 17 reptile species, including 6 snakes. It is accessible text that explores animal behavior and other interesting facts. It provides a brief and informative introduction to the habitats of the Masai Mara.8b:T66e,Before the twentieth century, personal debt resided on the fringes of the American economy, the province of small-time criminals and struggling merchants. By the end of the century, however, the most profitable corporations and banks in the country lent money to millions of American debtors. How did this happen? The first book to follow the history of personal debt in modern America, Debtor Nation traces the evolution of debt over the course of the twentieth century, following its transformation from fringe to mainstream--thanks to federal policy, financial innovation, and retail competition. How did banks begin making personal loans to consumers during the Great Depression? Why did the government invent mortgage-backed securities? Why was all consumer credit, not just mortgages, tax deductible until 1986? Who invented the credit card? Examining the intersection of government and business in everyday life, Louis Hyman takes the reader behind the scenes of the institutions that made modern lending possible: the halls of Congress, the boardrooms of multinationals, and the back rooms of loan sharks.
America's newfound indebtedness resulted not from a culture in decline, but from changes in the larger structure of American capitalism that were created, in part, by the choices of the powerful--choices that made lending money to facilitate consumption more profitable than lending to invest in expanded production. From the origins of car financing to the creation of subprime lending, Debtor Nation presents a nuanced history of consumer credit practices in the United States and shows how little loans became big business.8c:T5f3,

A guide to mastering microeconomic theory

Microeconomic Foundations I develops the choice, price, and general equilibrium theory topics typically found in first-year theory sequences, but in deeper and more complete mathematical form than most standard texts provide. The objective is to take the reader from acquaintance with these foundational topics to something closer to mastery of the models and results connected to them.

Provides a rigorous treatment of some of the basic tools of economic modeling and reasoning, along with an assessment of the strengths and weaknesses of these tools
Complements standard texts
Covers choice, preference, and utility; structural properties of preferences and utility functions; basics of consumer demand; revealed preference and Afriat's Theorem; choice under uncertainty; dynamic choice; social choice and efficiency; competitive and profit-maximizing firms; expenditure minimization; demand theory (duality methods); producer and consumer surplus; aggregation; general equilibrium; efficiency and the core; GET, time, and uncertainty; and other topics
Features a free web-based student's guide, which gives solutions to approximately half the problems, and a limited-access instructor's manual, which provides solutions to the rest of the problems
Contains appendixes that review most of the specific mathematics employed in the book, including a from-first-principles treatment of dynamic programming

8d:T54b,

An inside look at how one of the country’s most elite private schools prepares its students for success

As one of the most prestigious high schools in the nation, St. Paul's School in Concord, New Hampshire, has long been the exclusive domain of America's wealthiest sons. But times have changed. Today, a new elite of boys and girls is being molded at St. Paul's, one that reflects the hope of openness but also the persistence of inequality.

In Privilege, Shamus Khan returns to his alma mater to provide an inside look at an institution that has been the private realm of the elite for the past 150 years. He shows that St. Paul's students continue to learn what they always have—how to embody privilege. Yet, while students once leveraged the trappings of upper-class entitlement, family connections, and high culture, current St. Paul's students learn to succeed in a more diverse environment. To be the future leaders of a more democratic world, they must be at ease with everything from highbrow art to everyday life—from Beowulf to Jaws—and view hierarchies as ladders to scale. Through deft portrayals of the relationships among students, faculty, and staff, Khan shows how members of the new elite face the opening of society while still preserving the advantages that allow them to rule.

8e:T56e,The Princeton Guide to Ecology is a concise, authoritative one-volume reference to the field's major subjects and key concepts. Edited by eminent ecologist Simon Levin, with contributions from an international team of leading ecologists, the book contains more than ninety clear, accurate, and up-to-date articles on the most important topics within seven major areas: autecology, population ecology, communities and ecosystems, landscapes and the biosphere, conservation biology, ecosystem services, and biosphere management. Complete with more than 200 illustrations (including sixteen pages in color), a glossary of key terms, a chronology of milestones in the field, suggestions for further reading on each topic, and an index, this is an essential volume for undergraduate and graduate students, research ecologists, scientists in related fields, policymakers, and anyone else with a serious interest in ecology. * Explains key topics in one concise and authoritative volume * Features more than ninety articles written by an international team of leading ecologists * Contains more than 200 illustrations, including sixteen pages in color * Includes glossary, chronology, suggestions for further reading, and index * Covers autecology, population ecology, communities and ecosystems, landscapes and the biosphere, conservation biology, ecosystem services, and biosphere management8f:T58e,Guesstimation 2.0 reveals the simple and effective techniques needed to estimate virtually anything--quickly--and illustrates them using an eclectic array of problems. A stimulating follow-up to Guesstimation, this is the must-have book for anyone preparing for a job interview in technology or finance, where more and more leading businesses test applicants using estimation questions just like these. The ability to guesstimate on your feet is an essential skill to have in today's world, whether you're trying to distinguish between a billion-dollar subsidy and a trillion-dollar stimulus, a megawatt wind turbine and a gigawatt nuclear plant, or parts-per-million and parts-per-billion contaminants. Lawrence Weinstein begins with a concise tutorial on how to solve these kinds of order of magnitude problems, and then invites readers to have a go themselves. The book features dozens of problems along with helpful hints and easy-to-understand solutions. It also includes appendixes containing useful formulas and more. Guesstimation 2.0 shows how to estimate everything from how closely you can orbit a neutron star without being pulled apart by gravity, to the fuel used to transport your food from the farm to the store, to the total length of all toilet paper used in the United States.
It also enables readers to answer, once and for all, the most asked environmental question of our day: paper or plastic?90:T516,

A masterful overview of the philosophy of language from one of its most important thinkers

In this book one of the world's foremost philosophers of language presents his unifying vision of the field—its principal achievements, its most pressing current questions, and its most promising future directions. In addition to explaining the progress philosophers have made toward creating a theoretical framework for the study of language, Scott Soames investigates foundational concepts—such as truth, reference, and meaning—that are central to the philosophy of language and important to philosophy as a whole. The first part of the book describes how philosophers from Frege, Russell, Tarski, and Carnap to Kripke, Kaplan, and Montague developed precise techniques for understanding the languages of logic and mathematics, and how these techniques have been refined and extended to the study of natural human languages. The book then builds on this account, exploring new thinking about propositions, possibility, and the relationship between meaning, assertion, and other aspects of language use.

An invaluable overview of the philosophy of language by one of its most important practitioners, this book will be essential reading for all serious students of philosophy.

91:T613,In this prequel to the now-classic Makers of Modern Strategy, Victor Davis Hanson, a leading scholar of ancient military history, gathers prominent thinkers to explore key facets of warfare, strategy, and foreign policy in the Greco-Roman world. From the Persian Wars to the final defense of the Roman Empire, Makers of Ancient Strategy demonstrates that the military thinking and policies of the ancient Greeks and Romans remain surprisingly relevant for understanding conflict in the modern world. The book reveals that much of the organized violence witnessed today--such as counterterrorism, urban fighting, insurgencies, preemptive war, and ethnic cleansing--has ample precedent in the classical era. The book examines the preemption and unilateralism used to instill democracy during Epaminondas's great invasion of the Peloponnesus in 369 BC, as well as the counterinsurgency and terrorism that characterized Rome's battles with insurgents such as Spartacus, Mithridates, and the Cilician pirates.
The collection looks at the urban warfare that became increasingly common as more battles were fought within city walls, and follows the careful tactical strategies of statesmen as diverse as Pericles, Demosthenes, Alexander, Pyrrhus, Caesar, and Augustus. Makers of Ancient Strategy shows how Greco-Roman history sheds light on wars of every age. In addition to the editor, the contributors are David L. Berkey, Adrian Goldsworthy, Peter J. Heather, Tom Holland, Donald Kagan, John W. I. Lee, Susan Mattern, Barry Strauss, and Ian Worthington.92:T651,How government can forge dynamic public-private partnershipsAll too often government lacks the skill, the will, and the wallet to meet its missions. Schools fall short of the mark while roads and bridges fall into disrepair. Health care costs too much and delivers too little. Budgets bleed red ink as the cost of services citizens want outstrips the taxes they are willing to pay. Collaborative Governance is the first book to offer solutions by demonstrating how government at every level can engage the private sector to overcome seemingly insurmountable problems and achieve public goals more effectively.John Donahue and Richard Zeckhauser show how the public sector can harness private expertise to bolster productivity, capture information, and augment resources. The authors explain how private engagement in public missions―rightly structured and skillfully managed―is not so much an alternative to government as the way smart government ought to operate. The key is to carefully and strategically grant discretion to private entities, whether for-profit or nonprofit, in ways that simultaneously motivate and empower them to create public value. Drawing on a host of real-world examples-including charter schools, job training, and the resurrection of New York's Central Park―they show how, when, and why collaboration works, and also under what circumstances it doesn't.Collaborative Governance reveals how the collaborative approach can be used to tap the resourcefulness and entrepreneurship of the private sector, and improvise fresh, flexible solutions to today's most pressing public challenges.93:T694,Ever since Carl Sagan first predicted that extraterrestrial civilizations must number in the millions, the search for life on other planets has gripped our imagination. Is Earth so rare that advanced life forms like us--or even the simplest biological organisms--are unique to the universe? How to Find a Habitable Planet describes how scientists are testing Sagan's prediction, and demonstrates why Earth may not be so rare after all. James Kasting has worked closely with NASA in its mission to detect habitable worlds outside our solar system, and in this book he introduces readers to the advanced methodologies being used in this extraordinary quest. He addresses the compelling questions that planetary scientists grapple with today: What exactly makes a planet habitable? What are the signatures of life astronomers should look for when they scan the heavens for habitable worlds? In providing answers, Kasting explains why Earth has remained habitable despite a substantial rise in solar luminosity over time, and why our neighbors, Venus and Mars, haven't.
If other Earth-sized planets endowed with enough water and carbon are out there, he argues, chances are good that some of those planets sustain life. Kasting describes the efforts under way to find them, and predicts that future discoveries will profoundly alter our view of the universe and our place in it. This book is a must-read for anyone who has ever dreamed of finding other planets like ours--and perhaps even life like ours--in the cosmos. In a new afterword, Kasting presents some recent breakthroughs in the search for exoplanets and discusses the challenges facing space programs in the near future.94:T5c3,"Philosophical Logic" is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances the philosophical and technical aspects of the subject.The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. "Philosophical Logic" provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading."Philosophical Logic" addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis.95:T5d2,How Machiavelli's Christianity shaped his political thoughtTo many readers of The Prince, Machiavelli appears to be deeply un-Christian or even anti-Christian, a cynic who thinks rulers should use religion only to keep their subjects in check. But in Machiavelli's God, Maurizio Viroli, one of the world's leading authorities on Machiavelli, argues that Machiavelli, far from opposing Christianity, thought it was crucial to republican social and political renewal―but that first it needed to be renewed itself. And without understanding this, Viroli contends, it is impossible to comprehend Machiavelli's thought.Viroli places Machiavelli in the context of Florence's republican Christianity, which was founded on the idea that the true Christian is a citizen who serves the common good. In this tradition, God participates in human affairs, supports and rewards those who govern justly, and desires men to make the earthly city similar to the divine one. Building on this tradition, Machiavelli advocated a religion of virtue, and he believed that, without this faith, free republics could not be established, defend themselves against corruption, or survive. Viroli makes a powerful case that Machiavelli, far from being a pagan or atheist, was a prophet of a true religion of liberty, a way of moral and political living that would rediscover and pursue charity and justice.The translation of this work has been funded by SEPS―Segretariato Europeo per le Pubblicazioni Scientifiche.96:T420,We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day. Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis. Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion.97:T521,Like his compositions, Milton Babbitt's writings about music have exerted an extraordinary influence on postwar music and thinking about music. In essays and public addresses spanning fifty years, Babbitt has grappled profoundly with central questions in the composition and apprehension of music. These writings range from personal memoirs and critical reviews to closely reasoned metatheoretical speculations and technical exegesis. In the history of music theory, there has been only a small handful of figures who have produced work of comparable stature. Taken as a whole, Babbitt's writings are not only an invaluable testimony to his thinking--a priceless primary source for the intellectual and cultural history of the second half of the twentieth century--but also a remarkable achievement in their own right. Prior to this collection, Babbitt's writings were scattered through a wide variety of journals, books, and magazines--many hard to find and some unavailable--and often contained typographical errors and editorial corruptions of various kinds. This volume of almost fifty pieces gathers, corrects, and annotates virtually everything of significance that Babbitt has written.
The result is complete, authoritative, and fully accessible--the definitive source of Babbitt's influential ideas.98:T6eb,The international controversy over who "owns" antiquities has pitted museums against archaeologists and source countries where ancient artifacts are found. In his book "Who Owns Antiquity?", James Cuno argued that antiquities are the cultural property of humankind, not of the countries that lay exclusive claim to them. Now in "Whose Culture?", Cuno assembles preeminent museum directors, curators, and scholars to explain for themselves what's at stake in this struggle - and why the museums' critics couldn't be more wrong. Source countries and archaeologists favor tough cultural property laws restricting the export of antiquities, have fought for the return of artifacts from museums worldwide, and claim the acquisition of undocumented antiquities encourages looting of archaeological sites. In "Whose Culture?", leading figures from universities and museums in the United States and Britain argue that modern nation-states have at best a dubious connection with the ancient cultures they claim to represent, and that archaeology has been misused by nationalistic identity politics.They explain why exhibition is essential to responsible acquisitions, why our shared art heritage trumps nationalist agendas, why restrictive cultural property laws put antiquities at risk from unstable governments - and more. Defending the principles of art as the legacy of all humankind and museums as instruments of inquiry and tolerance, "Whose Culture?" brings reasoned argument to an issue that for too long has been distorted by politics and emotionalism. In addition to the editor, the contributors are Kwame Anthony Appiah, Sir John Boardman, Michael F. Brown, Derek Gillman, Neil MacGregor, John Henry Merryman, Philippe de Montebello, David I. Owen, and James C.Y. Watt.99:T60c,Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula.
Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.3c:["$","$L7e",null,{"state":{"mutations":[],"queries":[{"dehydratedAt":1794082719647,"state":{"data":{"pages":[{"requestId":"9f70b46a-40fb-497f-a97c-2a47f33a2801","total":{"value":2903,"relation":"eq"},"rows":[{"entityType":"book","isbn":"9780691176390","id":1170809,"score":2,"position":1608,"book":{"id":1170809,"isbn":"9780691176390","created":"2026-09-29T23:19:05.000Z","title":"Democratic reason : politics, collective intelligence, and the rule of the many","description":"$83","htmlDescription":null,"pages":304,"language":"eng","depth":10,"height":15,"width":230,"weight":433,"edition":null,"publishDate":"2013","authorNames":"Hélène Landemore","publisherName":"Princeton University Press","format":"BC","category":null,"image":"https://book-info.studentapan.live/image/9780691176390-democratic-reason-politics-collective-intelligence-and-the-rule-of-the-many.jpg","highResImage":"https://book-info.studentapan.live/image/9780691176390-democratic-reason-politics-collective-intelligence-and-the-rule-of-the-many.jpg/org","imageFile":"9780691176390","isRemoved":null,"views":0,"editionGroupId":295152,"editionGroupState":"UNPUBLISHED","adsCount":null,"minPrice":null,"source":"book-info-service","minNewPrice":267,"varugruppCode":null,"isExercise":false,"inventory":null,"sellAsDigital":false,"editionGroupSearchEnabled":false}},{"entityType":"book","isbn":"9780691158334","id":142615,"score":2,"position":1609,"book":{"id":142615,"isbn":"9780691158334","created":"2015-12-24T23:00:00.000Z","title":"The aesthetics of architecture","description":"Architecture is distinguished from other art forms by its sense of function, its localized quality, its technique, its public and nonpersonal character, and its continuity with the decorative arts. 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