The King of Infinite Space

Euclid and His Elements

Author: David Berlinski

Publisher: Basic Books

ISBN: 0465038638

Category: Mathematics

Page: 176

View: 8793

Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid's Elements, arguably the most influential book in the history of mathematics In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid's axiomatic system, a method of proof still taught in classrooms around the world. Euclid's use of elemental logic—and the mathematical statements he and others built from it—have dramatically expanded the frontiers of human knowledge. The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world.

The King of Infinite Space

Euclid and His Elements

Author: David Berlinski

Publisher: Hachette UK

ISBN: 0465038638

Category: Mathematics

Page: 176

View: 4980

Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid's Elements, arguably the most influential book in the history of mathematics In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid's axiomatic system, a method of proof still taught in classrooms around the world. Euclid's use of elemental logic—and the mathematical statements he and others built from it—have dramatically expanded the frontiers of human knowledge. The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world.

A Tour of the Calculus

Author: David Berlinski

Publisher: Vintage

ISBN: 9780307789730

Category: Mathematics

Page: 352

View: 7783

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review From the Trade Paperback edition.

Infinite Ascent

A Short History of Mathematics

Author: David Berlinski

Publisher: Modern Library

ISBN: 9780307778178

Category: Mathematics

Page: 224

View: 571

In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure. Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt. The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors. From the Hardcover edition.

One, Two, Three

Absolutely Elementary Mathematics

Author: David Berlinski

Publisher: Vintage

ISBN: 1400079101

Category: Mathematics

Page: 210

View: 9009

Considers the fundamentals of such basics as the actual workings of addition and the nature of logic, revealing how the complexities of simple mathematics are essential to everyday life.

Sacred Mathematics

Japanese Temple Geometry

Author: Hidetoshi Fukagawa,Tony Rothman

Publisher: Princeton University Press

ISBN: 9780691127453

Category: Art

Page: 348

View: 6552

"An enchanting history of Japanese geometry--of a time and place where 'geometers did not cede place to poets.' This intersection of science and culture, of the mathematical, the artistic, and the spiritual, is packed, like circles within circles, with rewarding Aha! epiphanies that drive a mathematician's curiosity."--Siobhan Roberts, author of "King of Infinite Space" "Teachers will welcome this remarkable collection of mathematical problems, history, and art, which will enrich their curriculum and promote both logical thinking and critical evaluation. It is especially important that we maintain an interest in geometry, which needs, and for once gets, more than its share."--Richard Guy, coauthor of "The Book of Numbers" "This remarkable book provides a novel insight into the Japanese mathematics of the past few hundred years. It is fascinating to see the difference in mathematical style from that which we are used to in the Western world, but the book also elegantly illustrates the cross-cultural Platonic nature and profound beauty of mathematics itself."--Roger Penrose, author of "The Road to Reality" "A significant contribution to the history of mathematics. The wealth of mathematical problems--from the very simple to quite complex ones--will keep the interested reader busy for years. And the beautiful illustrations make this book a work of art as much as of science. Destined to become a classic!"--Eli Maor, author of "The Pythagorean Theorem: A 4,000-Year History" "A pleasure to read. "Sacred Mathematics" brings to light the unique style and character of geometry in the traditional Japanese sources--in particular the "sangaku" problems. These problems range from trivial to utterly devilish. I found myself captivated by them, and regularly astounded by the ingenuity and sophistication of many of the traditional solutions."--Glen Van Brummelen, coeditor of "Mathematics and the Historian's Craft"

The Advent of the Algorithm

The 300-Year Journey from an Idea to the Computer

Author: David Berlinski

Publisher: Houghton Mifflin Harcourt

ISBN: 9780156013918

Category: Computers

Page: 345

View: 8094

Describes the invention of the algorithm, first theorized by Leibniz, and the dramatic implications of this mathematical discovery on the development of computer technology and the working of DNA.

King of Infinite Space

Donald Coxeter, the Man Who Saved Geometry

Author: Siobhan Roberts

Publisher: Bloomsbury Publishing USA

ISBN: 9780802718327

Category: Biography & Autobiography

Page: 416

View: 5143

"There is perhaps no better way to prepare for the scientific breakthroughs of tomorrow than to learn the language of geometry." -Brian Greene, author of The Elegant Universe The word "geometry" brings to mind an array of mathematical images: circles, triangles, the Pythagorean Theorem. Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives-from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century. Many of the greatest names in intellectual history-Pythagoras, Plato, Archimedes, Euclid- were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions-his famed Coxeter groups and Coxeter diagrams-have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational. Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.

The Music of the Republic

Essays on Socrates' Conversations and Plato's Writings

Author: Eva Brann

Publisher: Paul Dry Books

ISBN: 1589882814

Category: Philosophy

Page: 378

View: 4428

In this collection of essays, Eva Brann talks with readers about the conversations Socrates has with his fellow Athenians. She shows how Plato's dialogues and the timeless matters they address remain important to us today. From introductory pieces on the Republic, the Phaedo, and the Sophist, to an account of the less well known Charmides, each essay starts where Plato starts, without presupposing a critical theory. In the title essay's brilliant account of the Republic, Brann demonstrates its central importance in Plato's work. Other essays consider Plato's notion of time; discuss how to teach Plato to undergraduates; and contend that a thoughtful text-based study of Plato can have a very personal impact on a reader. Encouraged to befriend the dialogues, readers will join in the great Socratic conversations.

Mathematics and Its History

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 144196052X

Category: Mathematics

Page: 662

View: 4428

From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Newton's Gift

How Sir Isaac Newton Unlocked the System of the World

Author: David Berlinski

Publisher: Simon and Schuster

ISBN: 0684843927

Category: Biography & Autobiography

Page: 217

View: 7332

A portrait of the physicist's life assesses his remarkable accomplishments in the field of science, his rescue of the British mint and its currency, and his intellectual battles with his colleagues.

Euclid's Window

The Story of Geometry from Parallel Lines to Hyperspace

Author: Leonard Mlodinow

Publisher: Simon and Schuster

ISBN: 9781439135372

Category: Science

Page: 320

View: 8581

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

The Devil's Delusion

Atheism and Its Scientific Pretensions

Author: David Berlinski

Publisher: ReadHowYouWant.com

ISBN: 1458758567

Category: Religion

Page: 290

View: 1960

A secular Jew, Berlinski nonetheless delivers a biting defense of religious thought. This incisive book explores the limits of science and the pretensions of those who insist it can be--indeed must be--the ultimate touchstone for understanding the world--Cf publisher's description.

An Episodic History of Mathematics

Mathematical Culture Through Problem Solving

Author: Steven G. Krantz

Publisher: MAA

ISBN: 0883857669

Category: Mathematics

Page: 381

View: 6431

An Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematicsboth classical and modern.Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincar, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists.This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practicalgetting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on.This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process.

The Great Mathematical Problems

Author: Ian Stewart

Publisher: Profile Books

ISBN: 1847653510

Category: Mathematics

Page: 340

View: 2275

There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Infinitesimal

Author: Amir Alexander

Publisher: Oneworld Publications

ISBN: 1780745338

Category: Science

Page: 368

View: 395

On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.