Changing Views on Ancient Near Eastern Mathematics

Jens Hoyrup e Peter Damerow 

 Dietrich Reimer Verlag | 2001 | 316 páginas | pdf | 13 Mb

link
link1 

TABLE OF CONTENTS
Jens Hoyrup
Preface
An Editor's Personal Reminiscence ... VII
The Six Workshops . .. XV
Acknowledgments .... XVI
Robert K. Englund
Grain Accounting Practices in Archaic Mesopotamia
Hans Neumann
Zu den Buchungseintragen in den neusumerischen Handwerkerprasenzlisten aus Ur 37
Joachim Oelsner
HS 201 - Eine Reziprokentabelle der Ur III-Zeit . 53
Joran Friberg
Bricks and Mud in Metro-Mathematical Cuneiform Texts .. 61
Jens Hoyrup
The Old Babylonian Square Texts - BM 13901 and YBC 4714 Retranslation and Analysis 155
Peter Damerow
Kannten die Babylonier den Satz des Pythagoras? Epistemologische Anmerkungen zur Natur der babylonischen Mathematik. 219
Herrmann Hunger

Zeitmessung 311

Count Like an Egyptian: A Hands-on Introduction to Ancient Mathematics

David Reimer 

Princeton University Press | 2014 | 254 páginas | rar - pdf |10,6  Mb

link (password: matav)

The mathematics of ancient Egypt was fundamentally different from our math today. Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. In fact, it can't be understood using our current computational methods.Count Like an Egyptian provides a fun, hands-on introduction to the intuitive and often-surprising art of ancient Egyptian math. David Reimer guides you step-by-step through addition, subtraction, multiplication, and more. He even shows you how fractions and decimals may have been calculated--they technically didn't exist in the land of the pharaohs. You'll be counting like an Egyptian in no time, and along the way you'll learn firsthand how mathematics is an expression of the culture that uses it, and why there's more to math than rote memorization and bewildering abstraction.

Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you'll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing.

Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation--the precursor to our modern system--and compares ancient Egyptian mathematics to today's math, letting you decide for yourself which is better.

CONTENTS

Preface vii

Introduction ix

Computation Tables xi

1 Numbers 1

2 Fractions 13

3 Operations 22

4 Simplification 55

5 Techniques and Strategies 80

6 Miscellany 121

7 Base-Based Mathematics 144

8 Judgment Day 182

Practice Solutions 209

Index

Mathematics in Ancient and Medieval India

A. K. Bag

Chaukhamba Orientalia | 1979 | 353 páginas | rar - pdf | 8,43 Mb

link (password: matav)

The work in seven chapters is an account of the study and growth of Mathematics in India from Vedic times to c. 1800 A. D. In each of these chapters viz. Scholars of Mathematics, Arithmetic, Geometry, Alegebra, trigonometry, Infinitesimal Calculus and Trend of Indo-Persian and Arabic literature on Mathematics, an attempt has been made to present a critical assessment of the materials and trace Indian Originality and her role in the transmission of knowledge from one country to another. Many now topics, tools and techniques have been included and studied with proper references, which have not yet been discussed by earlier scholars. Besides, the work has been supplied with a General Bibliography to creat interest In the study and research in History of Mathematics. 

CONTENTS
INTRODUCTION
CHAPTER I- SCHOLARS OF MATHEMATICS 
CHAPTER II-ARITHMETIC
CHAPTER III-GEOMETRY
CHAPTER IV-ALGEBRA
CHAPTER V-TRIGONOMETRY
CHAPTER VI-INFINITESIMAL CALCULUS
CHAPTER VII-TREND OF INDO-PERSIAN ARABIC LITERATURE ON MATHEMATICSIN THE MEDIEVAL PERIOD

A Brief Guide to the Great Equations: The Hunt for Cosmic Beauty in Numbers

Robert Crease

Robinson Publishing | 2009 | 2727 páginas | epub | Mb

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mobi - 1,9 Mb - link

Here are the stories of the ten most popular equations of all time as voted for by readers of "Physics World", including - accessibly described here for the first time - the favourite equation of all, Euler's equation. Each is an equation that captures with beautiful simplicity what can only be described clumsily in words. Euler's equation [eip + 1 = 0] was described by respondents as 'the most profound mathematic statement ever written', 'uncanny and sublime', 'filled with cosmic beauty' and 'mind-blowing'. Collectively these equations also amount to the world's most concise and reliable body of knowledge. Many scientists and those with a mathematical bent have a soft spot for equations. This book explains both why these ten equations are so beautiful and significant, and the human stories behind them.

CONTENTS

Illustration Credits
Introduction
1   ‘The Basis of Civilization’: The Pythagorean Theorem
Interlude: Rules, Proofs, and the Magic of Mathematics
2   ‘The Soul of Classical Mechanics’: Newton’s Second Law of Motion
Interlude: The Book of Nature
3   ‘The High Point of the Scientific Revolution’: Newton’s Law of Universal Gravitation
Interlude: That Apple
4   ‘The Gold Standard for Mathematical Beauty’: Euler’s Equation
Interlude: Equations as Icons
5   The Scientific Equivalent of Shakespeare: The Second Law of Thermodynamics
Interlude: The Science of Impossibility
6   ‘The Most Significant Event of the Nineteenth Century’: Maxwell’s Equations
Interlude: Overcoming Anosognosia; or Restoring the Vitality of the Humanities
7   Celebrity Equation: E = mc2
Interlude: Crazy Ideas
8   The Golden Egg: Einstein’s Equation for General Relativity
Interlude: Science Critics
9   ‘The Basic Equation of Quantum Theory’: Schrödinger’s Equation
Interlude: The Double Consciousness of Scientists
10 Living with Uncertainty: The Heisenberg Uncertainty Principle
Interlude: The Yogi and the Quantum
Conclusion: Bringing the Strange Home
Notes
Acknowledgements
Index

Chinese Mathematical Astrology: Reaching out to the Stars

(Needham Research Institute Series)

Ho Peng Yoke

Routledge | 2013 | 228 páginas | rar - pdf | 8,19 Mb

link (password: matav)

Though there are a number of well-written works on Chinese divination, there are none that deal with the three sophisticated devices that were employed by the Chinese Astronomical Bureau in the eleventh century and for hundreds of years thereafter. Chinese experts applied the methods associated with these devices to both weather forecasting and to the interpretation of human affairs.
Hidden by a veil of secrecy, these methods have always been relatively little known other than by their names. The first work in any language to explore these three methods, known as sanshi (three cosmic boards), this book sheds light on a topic which has been shrouded in mystery for centuries, having been kept secret for many years by the Chinese Astronomical Bureau.

CONTENTS
List of figures viii
Preface xi
References to historical Chinese geographical names xvi
A brief note on Chinese romanization xxii
1 Introduction 1
2 Fundamental principles 12
3 The Taiyi system in the three cosmic boards: method of the Taiyi deity 36
4 Qimen Dunjia: Strange Gates Escaping Techniques 83
5 Liuren: the art of the six Yang Waters 113
Appendix I: traditional Chinese astrology 139
Appendix II: the Ziping method of fate-calculation 153
Appendix III: table of Chinese dynasties 165
Notes 167
Bibliography 179
Index 193

Mathematical Achievements of Pre-modern Indian Mathematicians

T.K Puttaswamy

Elsevier | 2012 | 768 páginas | rar - pdf |2,2 Mb 

link (password : matav)

pdf - 5,8 Mb - link

Mathematics in India has a long and impressive history. Presented in chronological order, this book discusses mathematical contributions of Pre-Modern Indian Mathematicians from the Vedic period (800 B.C.) to the 17^th Century of the Christian era. These contributions range across the fields of Algebra, Geometry and Trigonometry. The book presents the discussions in a chronological order, covering all the contributions of one Pre-Modern Indian Mathematician to the next. It begins with an overview and summary of previous work done on this subject before exploring specific contributions in exemplary technical detail. This book provides a comprehensive examination of pre-Modern Indian mathematical contributions that will be valuable to mathematicians and mathematical historians.

• Contains more than 160 original Sanskrit verses with English translations giving historical context to the contributions

• Presents the various proofs step by step to help readers understand

• Uses modern, current notations and symbols to develop the calculations and proofs

Contents
Preface
Foreword
Introduction
1 A Glance at Ancient India and the Decimal System of Numeration
2 The Sulvasutras
3 Mathematics of Jains
4 The Bakshali Manuscript
5 Aryabhata I
6 Varahamihira and Bhaskara I
7 Brahmagupta
8 Sridhara and Prthudakaswami Caturveda
9 Mahavira
10 Aryabhata II and Sripati
11 Bhaskara II
12 Narayana Pandita
13 Kerala Astronomers
14 Sixteenth and Seventeenth Century Commentators of Bhaskara II
Appendix
Bibliography

 

The Infinite in the Infinite

Alistair MacIntosh Wilson

OUP Oxford | 1995 | 539 páginas | pdf | 11 Mb

link

This book is an extended history of mathematics that places mathematical development firmly in its historical context. Each section begins with a description of the geography and history of the country considered. From there, lively retelling of the creation myths and legends leads on to a description of how its people wrote and counted. This is followed by relevant mathematical material. The book covers; 
* The geometry of stone circles in Europe * The area of triangles and volume of pyramids that concerned the engineers of the Pharoahs * The Babylonian sexagesimal number system and our present measures of space and time which grew out of it * The use of the abacus and remainder theory in China * Greek mathematics from Pythagoras to Pappus. Detailed accounts of the work of apollonius and Archimedes are given. * The invention of trigonometry by Arab mathematicians * The solution of quadratic equations by completing the square developed in India Each chapter has a mathematical case study which is discussed both in the context of thetimes and in th light of more recent developments. Worked examples are also included. 
"The author has woven together a broad historical backgrounding and some fairly detailed but accessible mathematics in amost exciting way." John Fauvel, author of Let Newton Be!


CONTENTS
Page
1 Symphonies of stone 1
2 The pyramid builders 19
3 The Theban Mysteries 42
4 Babylon
Babylonian mathematics 53
5 The Middle Kingdom 73
Chinese mathematics 73
6 The Achaeans 105
7 A world made of numbers 113
Pythagoras 113
The shapes of numbers 115
The regular polyhedra 118
Euler's number 124
Polyhedra in the world 128
8 The thoughts of Zeus 133
The symmetries of polygons 133
The symmetry groups of the regular polyhedra 142
9 The philosopher's criticism 163
Geometry 163
The Peloponnesian War 168
Socrates 171
Plato 175
Aristotle 181
Aristotle's logic 183
The Stoics construct the truth 196
10 The Elements of Euclid 207
Euclid's dream 208
Similar triangles 215
The angles of triangles 220
The area of a triangle 227
Pythagoras' theorem 230
Triangles in circles 233
11 An island interlude 239
12 Proportion 252
The geometrical solution of aha problems 252
The theory of proportion 252
The construction of regular polygons 260
The uses of proportion 268
A problem of maxima 274
13 The Divine Archimedes 279
Archimedes 279
The measurement of a circle 285
The method of exhaustion 293
The surface area of a sphere 297
The volume of a sphere 304
The volume of a cone 308
The quadrature of a spiral 312
The quadrature of a parabola 313
Archimedes' principle 317
The Rancher's Dilemma 321
14 Apollonius the great geometer 324
Apollonius 324
Apollonius' Conics 326
The three conic sections 327
Tangents to conic sections 335
The property of the parabola used by Archimedes 337
The centres of conics 343
The foci of a conic 348
Reflection properties of conic sections 355
The focal construction of conics 358
15 The science of numbers 367
Pythagorean numerology 367
Prime numbers 368
Irrational numbers 375
Pythagorean triples 380
Patterns of primes 383
16 The School of Alexandria 388
Alexandria 388
Heron 392
Diophantus 399
Pappus
The last of the Greeks
The Eudemian summary
17 The dark subcontinent of India
The Aryans
Sanskrit and the Hindu numerals
Hindu astronomy
The mathematics of Brahmagupta and Mahavira
A pearl of number theory
18 The contribution of Islam
The conquests of the Arabs
Trigonometry
The uses of trigonometry
The geometry of the sphere
The gnomon curve
Algebra
The summation of powers of integers
Spain under Islam
Bibliography
Index

The Ambitious Horse - Ancient Chinese Mathematics Problems

Lawrence Swienciki

Key Curriculum | 2000 | 135 páginas | pdf (no OCR) | 7,94 Mb

online: math.utep.edu


pdf (OCR) - 5,72 Mb - link

• Numbers and Arithmetic includes subjects such as Chinese writing; The Calculating Rods of Ancient China: and ancient Chinese multiplication.

• Geometry and Dissection problems includes subjects such as tangrams, the Measure of Heaven and Ancient Chinese Philosophy.

• Algebra Integrated with Geometry includes subjects such as Square Roots; Quadratic Equations; and mathematical treats such as the "Pillar of Delightful Contemplation", the "Exalted Treasure of Jade" and the "Precious Golden Rope".

On the one hand this book is far beyond what many 7th and 8th grader students are capable of. On the other hand, it is so interesting and so well done that it might just be that this is the book that helps transforms your child from a grudging math student to an enthusiastic one!

Filled with stories, puzzles and plenty of hands-on problems, this book is a treasure. It is divided into three sections:

Answers and solutions included.

Note: The problems get more difficult as the book progresses and so can be used for several years. Suitable for a very math-able 7th grader, a solid 8th grader and to enthuse and inspire high school students

Galileo's Muse: Renaissance Mathematics and the Arts

Mark A. Peterson

Harvard University Press | 2011 | páginas | rar - pdf | 829 kb

link (password: matav)

Mark Peterson makes an extraordinary claim in this fascinating book focused around the life and thought of Galileo: it was the mathematics of Renaissance arts, not Renaissance sciences, that became modern science. "Galileo's Muse" argues that painters, poets, musicians, and architects brought about a scientific revolution that eluded the philosopher-scientists of the day, steeped as they were in a medieval cosmos and its underlying philosophy. According to Peterson, the recovery of classical science owes much to the Renaissance artists who first turned to Greek sources for inspiration and instruction. Chapters devoted to their insights into mathematics, ranging from perspective in painting to tuning in music, are interspersed with chapters about Galileo's own life and work. Himself an artist turned scientist and an avid student of Hellenistic culture, Galileo pulled together the many threads of his artistic and classical education in designing unprecedented experiments to unlock the secrets of nature. In the last chapter, Peterson draws our attention to the Oratio de Mathematicae laudibus of 1627, delivered by one of Galileo's students. This document, Peterson argues, was penned in part by Galileo himself, as an expression of his understanding of the universality of mathematics in art and nature. It is 'entirely Galilean in so many details that even if it is derivative, it must represent his thought', Peterson writes. An intellectual adventure, "Galileo's Muse" offers surprising ideas that will capture the imagination of anyone - scientist, mathematician, history buff, lover of literature, or artist - who cares about the humanistic roots of modern science.

Contents
Prologue 1
1. Galileo, Humanist 3
2. The Classical Legacy 33
Poetry 67
3. The Plan of Heaven 69
4. The Vision of God 81
Painting 95
5. The Power of the Lines 99
6. The Skin of the Lion 125
Music 149
7. The Orphic Mystery 153
8. Kepler and the Music of the Spheres 174
Architecture 197
9. Figure and Form 203
10. The Dimensions of Hell 214
11. Mathematics Old and New 237
12. Transforming Mathematics 255
13. The Oration272
Epilogue 292
Notes 299
Acknowledgments 321
Index 323

From 0 to Infinity in 26 Centuries: The Extraordinary Story of Maths

Chris Waring

Michael O'Mara | 2012 | 192 páginas | epub | 2,8 Mb

link

We may remember their equations and discoveries from school, but do we remember who the men behind the math were? From the theories of Pythagoras (did you know he ran a secret brotherhood that studied maths, music, and gymnastics?) to coining the term "Googol," this book is packed full of fascinating facts and surprising stories from ancient times to the modern day. Do you want to know why the Ancient Greeks knew so much math? Or, why there was so little math studied in the Dark Ages? Read this fascinating book to uncover the mysteries of math.

Contents
Introduction
Prehistoric Maths
Early Civilized Maths
The Ancient Greeks
The Romans
Eastern Mathematics
The Middle Ages in Europe
The Renaissance Onwards
The Digital Age
Modern Mathematics
The Future of Mathematics
Bibliography

Mathematics and Measurement

 Oswald Ashton Wentworth Dilke

University of California Press | 1987 | 66 páginas

online: google books

pdf - 9,27 Mb - link

This fully illustrated book outlines the ancient systems of mathematics and measurement and describes how they were used in mapping, surveying, telling time, trade and commerce, as well as in leisure pursuits such as games and puzzles, and in the occult.

Contents
The Background 
2 Numbering by Letters 
1 Mathematical Education in the Greek World 
4. Measurement
5 Mathematics (or the Surveyor and Architect)
6 Mapping and the Concept of Scale 
7 Telling the Time
8. Calculatioos for Trade and Commerce
9. Mathematics in Leisure Pursuits and the Occult 
10 The Sequel 
Bibliography 62
Index 

War Games: A History of War on Paper

Philipp von von Hilgers e Ross Benjamin

The MIT Press | 2012 | 235 páginas | rar - pdf | 2,3 Mb

link (password: matav)

For centuries, both mathematical and military thinkers have used game-like scenarios to test their visions of mastering a complex world through symbolic operations. By the end of World War I, mathematical and military discourse in Germany simultaneously discovered the game as a productive concept. Mathematics and military strategy converged in World War II when mathematicians designed fields of operation. In this book, Philipp von Hilgers examines the theory and practice of war games through history, from the medieval game boards, captured on parchment, to the paper map exercises of the Third Reich. Von Hilgers considers how and why war games came to exist: why mathematical and military thinkers created simulations of one of the most unpredictable human activities on earth. Von Hilgers begins with the medieval rythmomachia, or Battle of Numbers, then reconstructs the ideas about war and games in the baroque period. He investigates the role of George Leopold von Reiswitz's tactical war game in nineteenth-century Prussia and describes the artifact itself: a game board--topped table with drawers for game implements. He explains Clausewitz's emphasis on the "fog of war" and the accompanying element of incalculability, examines the contributions of such thinkers as Clausewitz, Leibniz, Wittgenstein, and von Neumann, and investigates the war games of the German military between the two World Wars. Baudrillard declared this to be the age of simulacra; war games stand contrariwise as simulations that have not been subsumed in absolute virtuality.

Contents
Preface ix
Acknowledgments xiii
1 The Battle of Numbers in the Middle Ages 1
2 Power Games in the Baroque Period 11
3 The State of the War Game 31
4 Historiography in Real Time 57
5 Higher Mathematics and Nomos of the Earth 89
6 From Formula Games to the Universal Machine 103
Notes 145
Bibliography 175

Index 199

Circles Disturbed: The Interplay of Mathematics and Narrative

Apostolos Doxiadis e Barry Mazur

Princeton University Press | 2012 | 592 páginas | rar - pdf | 3,75 Mb

link (password: matav)
(novo formato)

epub | 6,7 Mb
link direto
link
link1

mobi - 8 Mb - link

Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--"Don't disturb my circles"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds--stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities.
A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.
In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier

CONTENTS
Introduction
1 From Voyagers to Martyrs: Toward a Storied History of Mathematics
AMIR ALEXANDER
2 Structure of Crystal, Bucket of Dust
PETER GALISON
3 Deductive Narrative and the Epistemological Function of Belief in Mathematics: On Bombelli and Imaginary Numbers
FEDERICA LA NAVE
4 Hilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics
COLIN MCLARTY
5 Do Androids Prove Theorems in Their Sleep?
MICHAEL HARRIS
6 Visions, Dreams, and Mathematics
BARRY MAZUR
7 Vividness in Mathematics and Narrative
TIMOTHY GOWERS
8 Mathematics and Narrative: Why Are Stories and Proofs Interesting?
BERNARD TEISSIER
9 Narrative and the Rationality of Mathematical Practice
DAVID CORFIELD
10 A Streetcar Named (among Other Things) Proof: From Storytelling to Geometry, via Poetry and Rhetoric
APOSTOLOS DOXIADIS
11 Mathematics and Narrative: An Aristotelian Perspective
G. E. R. LLOYD
12 Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative
ARKADY PLOTNITSKY
13 Formal Models in Narrative Analysis
DAVID HERMAN
14 Mathematics and Narrative: A Narratological Perspective
URI MARGOLIN
15 Tales of Contingency, Contingencies of Telling: Toward an Algorithm of Narrative Subjectivity
JAN CHRISTOPH MEISTER

Sugestão de tibu

Lost Discoveries: The Ancient Roots of Modern Science -- from the Babylonians to the Maya

Dick Teresi

Simon & Schuster | 2002 | 467 páginas | pdf |6,9  Mb

link

djvu - 2,7 Mb - link

Boldly challenging conventional wisdom, acclaimed science writer and Omni magazine cofounder Dick Teresi traces the origins of contemporary science back to their ancient roots in an eye-opening account and landmark work. 
This innovative history proves once and for all that the roots of modern science were established centuries, and in some instances millennia, before the births of Copernicus, Galileo, and Newton. In this enlightening, entertaining, and important book, Teresi describes many discoveries from all over the non-Western world -- Sumeria, Babylon, Egypt, India, China, Africa, Arab nations, the Americas, and the Pacific islands -- that equaled and often surpassed Greek and European learning in the fields of mathematics, astronomy, cosmology, physics, geology, chemistry, and technology. 
The first extensive and authoritative multicultural history of science written for a popular audience, Lost Discoveries fills a critical void in our scientific, cultural, and intellectual history and is destined to become a classic in its field.

Contents

1 A HISTORY OF SCIENCE: Rediscovered 1

2 MATHEMATICS: Tke Language of Science 21

3 ASTRONOMY Slcy Watckers and More 89

4 COSMOLOGY TW Old-Time Religion 157

5 PHYSICS: Particles, Voids, and Fields 193

6 GEOLOGY Stones of Eartk Itself 231

7 CHEMISTRY Alckemy and Beyond 279

8 TECHNOLOGY Mackines as a Measure of Man 325

Notes 369

Selected Bibliography 421

Acknowledgments 431

Index 433

Diophantos of Alexandria: A Study in the History of Greek Algebra

Thomas Little Heath

Cambridge, University press | 1985 | 298 páginas

online: ualberta.ca
archive.org
hathitrust.org
forgottenbooks.org

pdf - link (google books)

The Greek mathematician Diophantos of Alexandria lived during the third century CE. Apart from his age (he reached eighty-four), very little else is known about his life. Even the exact form of his name is uncertain, and only a few incomplete manuscripts of his greatest work, Arithmetica, have survived. In this impressive scholarly investigation, first published in 1885, Thomas Little Heath (1861-1940) meticulously presents what can be gleaned from Greek, Latin and Arabic sources, and guides the reader through the algebraist's idiosyncratic style of mathematics, discussing his notation and originality. This was the first thorough survey of Diophantos' work to appear in English. Also reissued in this series are Heath's two-volume History of Greek Mathematics, his treatment of Greek astronomy through the work of Aristarchus of Samos, and his edition in modern notation of the Treatise on Conic Sections by Apollonius of Perga.

O Último Teorema de Fermat

Simon Singh

Record | 2002 | 315 páginas | rar - pdf | 12,6 Mb

link (password : matav)

Com esta anotação incompleta, feita em 1637 no livro Aritmética, de Diofante, o matemático francês Pierre de Fermat, que morreu antes de descrever seu teorema, lançava o desafio que iria confundir e frustrar os matemáticos mais brilhantes do mundo por mais de 350 anos. O último teorema de Fermat, como ficou conhecido, tornou-se o Santo Graal da matemática. Vidas inteiras foram devotadas — algumas até mesmo sacrificadas — à demonstração de uma equação aparentemente simples. O livro é a história da busca épica para resolver um dos maiores enigmas de todos os tempos. Um drama humano de grandes sonhos, brilho intelectual e extraordinária determinação.
Leonhard Euler, o maior matemático do século XVIII, teve que admitir a derrota. Sophie Germain assumiu a identidade de um homem para poder pesquisar num campo que era fechado às mulheres, e conseguiu avanços significativos no século XIX. Évariste Galois passou a noite escrevendo os resultados de sua pesquisa, antes de morrer num duelo em 1832. Yutaka Taniyama, cujas descobertas levariam à solução do enigma, matou-se em 1958. Paul Wolfskehl, um famoso empresário alemão, criou um prêmio valioso para a primeira pessoa que demonstrasse o teorema.
Surgiu, então, um professor de Princeton, Andrew Wiles, que sonhava em demonstrar o último teorema de Fermat desde que o vira pela primeira vez, ainda menino, na biblioteca de sua cidade. Com medo da sucessão de fracassos de seus antecessores, durante sete anos publicou artigos sobre outros assuntos, de modo a despistar os colegas, enquanto trabalhava em sua obsessão. Em 1993, passados 356 anos desde o desafio de Fermat, Wiles assombrou o mundo ao anunciar a demonstração. Mas sua luta ainda não havia terminado. Um erro o fez voltar às pesquisas por mais 14 meses, até que, em 1995, ele ganhou as páginas de jornais do mundo inteiro e 50 mil libras da Fundação Wolfskehl.

The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context

Brian Evans

Wiley | 2014 | 248 páginas | rar - pdf | 1,3 Mb

link (password: matav)

With a balanced blend of formal history with anecdotes and legends, The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context takes readers on a journey throughout time in an effort to understand the patterns of quantity, structure, and dimensions found in the world. The author explores mathematics using a historical context and emphasizes that no single culture had a monopoly on mathematical advancements; rather, various groups influenced one another and developed simultaneously.

The book begins with the earliest known records of human mathematics in Africa and continues on to ancient Egypt and Babylon. The journey moves into ancient Greece, China and India, and the Islamic world. Next, the mathematics of the pre-Columbian Americas, the dark period of mathematics in Europe after the fall of the Roman Empire, and the influence of Islamic mathematics on European thinking are presented. The European Renaissance through the 17^th, 18^th, and 19^th centuries are explored, and the 20^th century takes readers through Europe and to North America, which took the lead in mathematics after World War II. Finally, readers are provided with a modern review of mathematics in the 21^stcentury, along with the history of mathematics education and its development in the United States. The book also features:

• Interesting and enjoyable anecdotes and mathematical legends

• Examples of parallels between the historical development of mathematical methods and everyday problem solving

• Major mathematical findings and contributions by significant historical figures

• Highlights and contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American

A useful textbook for undergraduate courses on the history of mathematics, The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context is also appropriate for elementary and secondary education majors. Presented in an easy-to-follow style, the book also serves as a resource for readers interested in the development of mathematics as a coherent discipline.

Contents

Introduction ix

PART 1 MATHEMATICS IN AFRICA AND THE

MEDITERRANEAN REGION 1

1 ANCIENT CIVILIZATION MATHEMATICS: AFRICA AS OUR BIRTHPLACE 3

2 ANCIENT EGYPTIAN MATHEMATICS: THE TIME OF THE PHARAOHS 7

3 BABYLONIAN MATHEMATICS: THE MESOPOTAMIAN CRADLE OF CIVILIZATION 17

4 GREEK MATHEMATICS: THE ARCHAIC PERIOD 25

5 GREEK MATHEMATICS: THE CLASSICAL PERIOD 37

6 GREEK MATHEMATICS: THE HELLENISTIC AND ROMAN/BYZANTINE PERIODS 45

PART 2 MATHEMATICS IN ASIA AND PRE-COLUMBIAN AMERICA 59

7 CHINESE MATHEMATICS: ANCIENT TIMES TO THE MIDDLE AGES 61

8 INDIAN MATHEMATICS: ANCIENT TIMES TO THE MIDDLE AGES 75

9 ISLAMIC MATHEMATICS: PRESERVATION, INNOVATION, AND CONNECTION BETWEEN EAST AND WEST 87

10 PRE-COLUMBIAN AMERICAN MATHEMATICS: THE OLMEC, MAYA, AND INCA CIVILIZATIONS 97

PART 3 MATHEMATICS IN EUROPE 105

11 EUROPEAN MATHEMATICS: THE MIDDLE AGES AND THE RENAISSANCE 107

12 EUROPEAN MATHEMATICS: THE 17TH CENTURY 123

13 EUROPEAN MATHEMATICS: THE 18TH CENTURY 143

14 EUROPEAN MATHEMATICS: THE 19TH CENTURY 157

PART 4 MATHEMATICS IN THE 20TH AND 21ST CENTURIES 175

15 EUROPEAN, AMERICAN, AND GLOBAL MATHEMATICS: THE 20TH AND 21ST CENTURIES 177

16 EUROPEAN, AMERICAN, AND GLOBAL MATHEMATICS: A SHIFT IN THE 20TH CENTURY 199

17 AMERICAN MATHEMATICS EDUCATION: THE 20TH AND 21ST CENTURIES 207

Resources and Recommended Readings 219

Index 221

El Enigma de Fermat

 

Simon Singh e Ana Herrera Ferrer 

Booket | 2004 | 320 páginas | pdf | 6,2 Mb

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4shared.com

Pierre de Fermat (1601-1665) planteó un problema que ha obsesionado a los matemáticos durante siglos. Éste libro es la magnífica historia de una búsqueda científica sin precedentes, llena de ingenio, inspiración y perseverancia. El último teorema de Fermat ha revelado, por fin, su secreto. Ha dejado de ser una obsesión. Ya no es un misterio.

Índice

Prólogo, por John Lynch 4

Prefacio 14

1. «Creo que lo dejaré aquí» 18

2. El retador 56

3. Una humillación matemática 96

4. Hacia la abstracción 152

5. Prueba por contradicción 212

6. El cálculo secreto 244

7. Un pequeño problema 296

8. La gran unificación de las matemáticas 320

Apéndices 352

Sugerencias 366

Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem

 Simon Singh

Fourth Estate | 1997 | 315 páginas | epub | 1,1 Mb

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mobi - 2 Mb - link

xn + yn = zn, where n represents 3, 4, 5, ...no solution

"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."
With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.


CONTENTS
Preface
1 ‘I Think I’ll Stop Here’
2 The Riddler
3 A Mathematical Disgrace
4 Into Abstraction
5 Proof by Contradiction
6 The Secret Calculation
7 A Slight Problem
Epilogue Grand Unified Mathematics
Appendices
Suggestions for Further Reading

Index

A Strange Wilderness: The Lives of the Great Mathematicians

Amir D. Aczel

Sterling | 2011 | 304 páginas | 304 páginas | rar - epub | 9,51 Mb

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“Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.”-- Mathematics historian W. S. Anglin

From the internationally bestselling author of Fermat's Last Theorem comes a landmark publication on the eccentric lives of the foremost mathematicians in history..
From Archimedes' eureka moment to Alexander Grothendieck's seclusion in the Pyrenees, bestselling author Amir Aczel selects the most compelling stories in the history of mathematics, creating a colorful narrative that explores the quirky personalities behind some of the most groundbreaking, enduring theorems.
This is not your dry “college textbook” account of mathematical history; it bristles with tales of duels, battlefield heroism, flamboyant arrogance, pranks, secret societies, imprisonment, feuds, theft, and some very costly errors of judgment. (Clearly, genius doesn't guarantee street smarts.) Ultimately, readers will come away entertained, and with a newfound appreciation of the tenacity, complexity, eccentricity, and brilliance of the mathematical genius.

Contents
Hellenic foundations.
God is number ; Plato's Academy ; Alexandria
The East.
The House of Wisdom ; Medieval China
Renaissance mathematics.
Italian shenanigans ; Heresy
To calculus and beyond.
The gentleman soldier ; The greatest rivalry ; Geniuses of the Enlightenment
Upheaval in France.
Napoleon's mathematicians ; Duel at dawn
Toward a new mathematics.
Infinity and mental illness ; Unlikely heroes ; The strangest wilderness.