Euclid—The Creation of Mathematics

Author: Benno Artmann

Publisher: Springer Science & Business Media

ISBN: 1461214122

Category: Mathematics

Page: 349

View: 4214

Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.
Posted in Mathematics

Euclid—The Creation of Mathematics

Author: N.A

Publisher: Springer

ISBN: 9780387984230

Category: Mathematics

Page: 343

View: 6700

Written by an authority on the history of Greek mathematics, as well as outstanding geometer, this book on the beginnings of mathematics is clearly written, interesting, and insightful--giving a fresh look at the subject. With the current interest in Euclid, this accessible presentation should interest a wide audience. 116 illus.
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The Mathematics of Plato's Academy

A New Reconstruction

Author: D. H. Fowler

Publisher: Oxford University Press on Demand

ISBN: 9780198502586

Category: Mathematics

Page: 441

View: 928

In this new expanded edition, Fowler provides a detailed examination of the ancient texts related to the subject and gives a thought-provoking new interpretation. Among the features of this edition are an appendix, a new epilogue, and an updated bibliography.
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Elements of Mathematics

From Euclid to Gödel

Author: John Stillwell

Publisher: Princeton University Press

ISBN: 1400880564

Category: Mathematics

Page: 440

View: 5339

Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.
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The Elements of Euclid

Author: Euclid

Publisher: N.A


Category: Geometry

Page: 416

View: 353

Posted in Geometry

Here's Looking at Euclid

A Surprising Excursion Through the Astonishing World of Math

Author: Alex Bellos

Publisher: Simon and Schuster

ISBN: 1416596348

Category: Mathematics

Page: 336

View: 444

Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place." Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct—including the revelation that ants can actually count how many steps they’ve taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games. Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here’s Looking at Euclid is a rare gem that brings the beauty of math to life.
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The First Book of Euclid's Elements

With a Commentary Based Principally Upon that of Proclus Diadochus

Author: Euclid,Proclus

Publisher: N.A


Category: Euclid's Elements

Page: 139

View: 5009

Posted in Euclid's Elements

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: 3839

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.
Posted in Science

Exploring Advanced Euclidean Geometry with GeoGebra

Author: Gerard A. Venema

Publisher: MAA

ISBN: 0883857847

Category: Mathematics

Page: 129

View: 6367

This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincaré disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry. The text consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. First the ideas are explored at the computer and then those ideas are assembled into a proof of the result under investigation. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.
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The Mathematics of Harmony

Author: N.A

Publisher: N.A

ISBN: 9814472573


Page: N.A

View: 2264

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Geometry: Euclid and Beyond

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 0387226761

Category: Mathematics

Page: 528

View: 4914

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Posted in Mathematics

An Episodic History of Mathematics

Mathematical Culture Through Problem Solving

Author: Steven G. Krantz

Publisher: MAA

ISBN: 0883857669

Category: Mathematics

Page: 381

View: 2391

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.
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The Great Geometer

Author: Chris Hayhurst

Publisher: The Rosen Publishing Group, Inc

ISBN: 9781404204973

Category: Juvenile Nonfiction

Page: 112

View: 4216

Biography of Greek mathematician Euclid describing the lasting influence he has had on the field of geometry.
Posted in Juvenile Nonfiction

The King of Infinite Space

Euclid and His Elements

Author: David Berlinski

Publisher: Basic Books

ISBN: 0465038638

Category: Mathematics

Page: 176

View: 6408

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.
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Euclid's Elements

all thirteen books complete in one volume : the Thomas L. Heath translation

Author: Euclid,Dana Densmore

Publisher: Green Lion Pr


Category: Mathematics

Page: 499

View: 4464

The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy sewn hardcover student and teacher edition in one volume, with minimal notes and a new index/glossary.
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Mathematical Thought From Ancient to Modern Times

Author: Morris Kline

Publisher: Oxford University Press

ISBN: 0199770468

Category: Mathematics

Page: 432

View: 6473

The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.
Posted in Mathematics

The Father of Geometry

Euclid and His 3-D World

Author: Paul W. Hightower

Publisher: Enslow Publishing, LLC

ISBN: 9780766034099

Category: Juvenile Nonfiction

Page: 112

View: 2079

"A biography of ancient Greek mathematician Euclid, known as the father of geometry and author of the mathematics textbook Elements"--Provided by publisher.
Posted in Juvenile Nonfiction

An Essay on the Psychology of Invention in the Mathematical Field

Author: Jacques Hadamard

Publisher: Read Books Ltd

ISBN: 1447493273

Category: Mathematics

Page: 164

View: 1032

Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
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Loving and Hating Mathematics

Challenging the Myths of Mathematical Life

Author: Reuben Hersh,Vera John-Steiner

Publisher: Princeton University Press

ISBN: 9781400836116

Category: Mathematics

Page: 432

View: 9110

Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.
Posted in Mathematics