Trigonometry For Dummies

Mary Jane Sterling

 For Dummies | 2014 - 2ª edição | 387 páginas | rar - pdf | 4 Mb


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A plain-English guide to the basics of trig

Trigonometry deals with the relationship between the sides and angles of triangles... mostly right triangles. In practical use, trigonometry is a friend to astronomers who use triangulation to measure the distance between stars. Trig also has applications in fields as broad as financial analysis, music theory, biology, medical imaging, cryptology, game development, and seismology.

From sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English and offering lots of easy-to-grasp example problems. It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers.

• Tracks to a typical Trigonometry course at the high school or college level

• Packed with example trig problems

• From the author of Trigonometry Workbook For Dummies

Trigonometry For Dummies is for any student who needs an introduction to, or better understanding of, high-school to college-level trigonometry.

Contents at a Glance

Introduction........ 1

Part I: Getting Started with Trigonometry......... 5

Chapter 1: Trouncing Trig Technicalities..........7

Chapter 2: Coordinating Your Efforts with Cartesian Coordinates...29

Chapter 3: Functioning Well...............47

Chapter 4: Getting Your Degree.............57

Chapter 5: Dishing Out the Pi: Radians.........67

Chapter 6: Getting It Right with Triangles...........81

Part II: Trigonometric Functions........... 91

Chapter 7: Doing Right by Trig Functions..................93

Chapter 8: Trading Triangles for Circles: Circular Functions....109

Chapter 9: Defining Trig Functions Globally........121

Chapter 10: Applying Yourself to Trig Functions............135

Part III: Identities...... 155

Chapter 11: Identifying Basic Identities.......157

Chapter 12: Operating on Identities..........171

Chapter 13: Proving Identities: The Basics..........189

Chapter 14: Sleuthing Out Identity Solutions.........207

Part IV: Equations and Applications........ 223

Chapter 15: Investigating Inverse Trig Functions........225

Chapter 16: Making Inverse Trig Work for You.....233

Chapter 17: Solving Trig Equations........243

Chapter 18: Obeying the Laws.........265

Part V: The Graphs of Trig Functions..... 289

Chapter 19: Graphing Sine and Cosine...........291

Chapter 20: Graphing Tangent and Cotangent........307

Chapter 21: Graphing Other Trig Functions.......317

Chapter 22: Topping Off Trig Graphs........329
Part VI: The Part of Tens.................. 343
Chapter 23: Ten Basic Identities . . . Plus Some Bonuses....345
Chapter 24: Ten Not-So-Basic Identities............349
Appendix: Trig Functions Table......... 353
Index........ 357

Livro relacionado:

Trigonometry workbook for dummies por Mary Jane Sterling Idioma: Inglês   Editora: Hoboken, N.J. ; [Great Britain] : Wiley, ©2005.

Seduced by Logic: Emilie Du Chatelet, Mary Somerville and the Newtonian Revolution

 Robyn Arianrhod

 Oxford University Press | 2012 | 345 páginas | rar - pdf | 943 kb

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Newton's explanation of the natural law of universal gravity shattered the way mankind perceived the universe, and hence it was not immediately embraced. After all, how can anyone warm to a force that cannot be seen or touched? But for two women, separated by time and space but joined in their passion for Newtonian physics, the intellectual power of that force drove them to great achievements. Brilliant, determined, and almost entirely self-taught, they dedicated their lives to explaining and disseminating Newton's discoveries.
Robyn Arianrhod's Seduced by Logic tells the story of Emilie du Chatelet and Mary Somerville, who, despite living a century apart, were connected by their love for mathematics and their places at the heart of the most advanced scientific society of their age. When Newton published his revolutionary theory of gravity, in his monumental Principia of 1687, most of his Continental peers rejected it for its reliance on physical observation and mathematical insight instead of religious or metaphysical hypotheses. But the brilliant French aristocrat and intellectual Emilie du Chatelet and some of her early eighteenth-century Enlightenment colleagues--including her lover, Voltaire--realized the Principia had changed everything, marking the beginning of theoretical science as a predictive, quantitative, and secular discipline. Emilie devoted herself to furthering Newton's ideas in France, and her translation of the Principia is still the accepted French version of this groundbreaking work. Almost a century later, in Scotland, Mary Somerville taught herself mathematics and rose from genteel poverty to become a world authority on Newtonian physics. She was fêted by the famous French Newtonian, Pierre Simon Laplace, whose six-volume Celestial Mechanics was considered the greatest intellectual achievement since the Principia. Laplace's work was the basis of Mary's first book, Mechanism of the Heavens; it is a bittersweet irony that this book, written by a woman denied entry to university because of her gender, remained an advanced university astronomy text for the next century. 
Combining biography, history, and popular science, Seduced by Logic not only reveals the fascinating story of two incredibly talented women, but also brings to life a period of dramatic political and scientific change. With lucidity and skill, Arianrhod explains the science behind the story, and explores - through the lives of her protagonists - the intimate links between the unfolding Newtonian revolution and the development of intellectual and political liberty.

CONTENTS
Introduction 1
1 Madame Newton du Châtelet 6
2 Creating the theory of gravity: the Newtonian controversy 12
3 Learning mathematics and fighting for freedom 20
4 Émilie and Voltaire’s Academy of Free Thought 37
5 Testing Newton: the ‘New Argonauts’ 56
6 The danger in Newton: life, love and politics 67
7 The nature of light: Émilie takes on Newton 80
8 Searching for ‘energy’: Émilie discovers Leibniz 97
9 Mathematics and free will 114
10 The re-emergence of Madame Newton du Châtelet 132
11 Love letters to Saint-Lambert 147
12 Mourning Émilie 155
13 Mary Fairfax Somerville 161
14 The long road to fame 175
15 Mechanism of the Heavens 197
16 Mary’s second book: popular science in the nineteenth century 214
17 Finding light waves: the ‘Newtonian Revolution’ comes of age 227
18 Mary Somerville: a fortunate life 244
Epilogue: Declaring a point of view 252
Appendix 258
Notes and Sources 286
Bibliography 318
Acknowledgments 328
Index 329

Geometry from Euclid to Knots

(Dover Books on Mathematics)

Saul Stahl

Dover Publications | 2010 | 480 páginas | rar - epub | 22,7 Mb

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Designed to inform readers about the formal development of Euclidean geometry and to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text closely follows Euclid's classic, Elements. The text augments Euclid's statements with appropriate historical commentary and many exercises — more than 1,000 practice exercises provide readers with hands-on experience in solving geometrical problems.

In addition to providing a historical perspective on plane geometry, this text covers non-Euclidean geometries, allowing students to cultivate an appreciation of axiomatic systems. Additional topics include circles and regular polygons, projective geometry, symmetries, inversions, knots and links, graphs, surfaces, and informal topology. This republication of a popular text is substantially less expensive than prior editions and offers a new Preface by the author.

Contents
Preface to the Dover Edition
Preface
1 Other Geometries: A Computational Introduction
1.1 Spherical Geometry
1.2 Hyperbolic Geometry
1.3 Other Geometries
2 The Neutral Geometry of the Triangle
2.1 Introduction
2.2 Preliminaries
2.3 Propositions 1 through 28
2.4 Postulate 5 Revisited
3 Nonneutral Euclidean Geometry
3.1 Parallelism
3.2 Area
3.3 The Theorem of Pythagoras
3.4 Consequences of the Theorem of Pythagoras
3.5 Proportion and Similarity
4. Circles and Regular Polygons
4.1 The Neutral Geometry of the Circle
4.2 The Nonneutral Euclidean Geometry of the Circle
4.3 Regular Polygons
4.4 Circle Circumference and Area
4.5 Impossible Constructions
5 Toward Projective Geometry
5.1 Division of Line Segments
5.2 Collinearity and Concurrence
5.3 The Projective Plane
6 Planar Symmetries
6.1 Translations, Rotations, and Fixed Points
6.2 Reflections
6.3 Glide Reflections
6.4 The Main Theorems
6.5 Symmetries of Polygons
6.6 Frieze Patterns
6.7 Wallpaper Designs
7 Inversions
7.1 Inversions as Transformations
7.2 Inversions to the Rescue
7.3 Inversions as Hyperbolic Motions
8 Symmetry in Space
8.1 Regular and Semiregular Polyhedra
8.2 Rotational Symmetries of Regular Polyhedra
8.3 Monstrous Moonshine
9. Informal Topology
10 Graphs
10.1 Nodes and Arcs
10.2 Traversability
10.3 Colorings
10.4 Planarity
10.5 Graph Homeomorphisms
11 Surfaces
11.1 Polygonal Presentations
11.2 Closed Surfaces
11.3 Operations on Surfaces
11.4 Bordered Surfaces
12 Knots and Links
12.1 Equivalence of Knots and Links
12.2 Labelings
12.3 The Jones Polynomial
Appendix A: A Brief Introduction to The Geometer's Sketchpad®
Appendix B: Summary of Propositions
Appendix C: George D. Birkhoff's Axiomatization of Euclidean Geometry
Appendix D: The University of Chicago School Mathematics Project's Geometrical Axioms
Appendix E: David Hilbert's Axiomatization of Euclidean Geometry

The Humongous Book of SAT Math Problems

 

W. Michael Kelley

ALPHA | 2013 | páginas | rar - pdf | 10,6 Mb

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Translated for people who don't speak math! The Humongous Book of SAT Math Problems takes a typical SAT study guide of solved math problems and provides easy-to-follow margin notes that add missing steps and simplify the solutions, thereby better preparing students to solve all types of problems that appear in both levels of the SAT math exam. Award-winning teacher, Mike Kelley, offers 750 problems with step-by-step notes and comprehensive solutions. The Humongous Books are like no other math guide series!

Le nombre d'or

Marius Cleyet-Michaud

Presses Universitaires de France | 1973 | 132 páginas | rar - djvu | 1.33 Mb

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Mystérieuse expression qui revient fréquemment dans les propos des artistes et des poètes, grandeur arithmétique authentique, le nombre d’or renferme-t-il, comme le croient certains, la clef de la connaissance ? Cet ouvrage se propose de présenter à tous ceux que le nombre d’or séduit ou intrigue un ensemble de faits positifs, sans pour autant se borner aux propriétés mathématiques de ce nombre qui sert à désigner à la fois une grandeur physique (plus précisément astronomique) et une grandeur purement arithmétique (à laquelle on attribue certaines propriétés esthétiques).
Quelle est l’histoire de l’invention de cette « divine proportion » et de ses applications, en mathématique, dans l’art (peinture, musique, poésie) ou l’architecture ? Quelle mystique a-t-elle inspiré ?

TABLE DES MATIÈRES 
Introduction
PREMIÈRE PARTIE  QU'EST-CE QUE LE NOMBRE D'OR? 
Chapitre 1 - n y a nombre d'or et nombre d'or
Chapitre II - Aperçu historique
Chapitre III - Mystique et symbolique
DEUXIÈME PARTIE  LE NOMBRE D'OR, ÊTRE MATHÉMATIQUE 
Chapitre 1 - Géométrie du nombre d'or
Chapitre II - Aritlunétique et algèbre
TROISIÈME PARTIE
LE NOMBRE D'OR DANS LA NATURE ET DANS L'ART 
Chapitre 1 - Le nombre d'or et les phénomènes naturels 81
Chapitre II - Les arts de la durée 89
Chapitre III - Les arts de l'espace 97
Conclusion 121
Bibliographie 125 

The Empire of Chance: How Probability Changed Science and Everyday Life

(Ideas in Context)

Gerd Gigerenzer, Zeno Swijtink, Theodore Porter, Lorraine Daston, John Beatty, Lorenz Kruger

Cambridge University Press | 1990 | 360 páginas | rar - pdf | 35,4 Mb

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This book tells how quantitative ideas of chance have transformed the natural and social sciences as well as everyday life over the past three centuries. A continuous narrative connects the earliest application of probability and statistics in gambling and insurance to the most recent forays into law, medicine, polling, and baseball. Separate chapters explore the theoretical and methodological impact on biology, physics, and psychology. In contrast to the literature on the mathematical development of probability and statistics, this book centers on how these technical innovations recreated our conceptions of nature, mind, and society.

CONTENTS
Acknowledgments page xi
Introduction xiii
1 Classical probabilities, 1660-1840 1
1.1 Introduction 1
1.2 The beginnings 2
1.3 The classical interpretation 6
1.4 Determinism 11
1.5 Reasonableness 14
1.6 Risk in gambling and insurance 19
1.7 Evidence and causes 26
1.8 The moral sciences 32
1.9 Conclusion 34
2 Statistical probabilities, 1820-1900 37
2.1 Introduction 37
2.2 Statistical regularity and l'homme moyen 38
2.3 Opposition to statistics 45
2.4 Statistics and variation 48
2.5 The error law and correlation 53
2.6 The statistical critique of determinism 59
2.7 Conclusion 68
3 The inference experts 70
3.1 In want of a "system of mean results" 70
3.2 Analysis of variance 73
3.3 Fisher's antecedents: early significance tests and comparative experimentation
3.4 The controversy: Fisher vs. Neyman and Pearson 90
3.5 Hybridization: the silent solution 106
3.6 The statistical profession: intellectual autonomy 109
3.7 The statistical profession: institutions and influence 115
3.8 Conclusion 120
4 Chance and life: controversies in modem biology 123
4.1 Introduction 123
4.2 Spontaneity and control: chance in physiology 124
4.3 Coincidence and design: chance in natural history 132
4.4 Correlations and causes: chance in genetics 141
4.5 Sampling and selection: chance in evolutionary biology 152
5 The probabilistic revolution in physics 163
5.1 The background: classical physics 163
5.2 Probability in classical physics: the epistemic interpretation
5.3 Three limitations of classical physics: sources of probabilism
5.4 Comments on the three limitations 175
5.5 Mass phenomena and propensities 179
5.6 Explanations from probabilistic assumptions 182
5.7 The puzzle of irreversibility in time 187
5.8 The discontinuity underlying all change 190
6 Statistics of the mind 203
6.1 Introduction 203
6.2 The pre-statistical period 204
6.3 The new tools 205
6.4 From tools to theories of mind 211
6.5 A case study: from thinking to judgments under uncertainty
6.6 The return of the reasonable man 226

6.7 Conclusion 233

Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method

Carlo Cellucci

Springer | 2013 | 391 páginas | rar - pdf | 1,9 Mb

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This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice.

Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically.

Contents

Preface.
Chapter 1. Introduction.
Part I. Ancient Perspectives.
Chapter 2. The Origin of Logic.
Chapter 3. Ancient Logic and Science
Chapter 4. The Analytic Method.
Chapter 5. The Analytic-Synthetic Method.
Chapter 6. Aristotle's Logic: The Deductivist View.
Chapter 7. Aristotle's Logic: The Heuristic View.
Part II. Modern Perspectives.
Chapter 8. The Method of Modern Science
Chapter 9. The Quest for a Logic of Discovery.
Chapter 10. Frege's Approach to Logic
Chapter 11. Gentzen's Approach to Logic.
Chapter 12. The Limitations of Mathematical Logic
Chapter 13. Logic, Method, and the Psychology of Discovery.
Part III: An Alternative Perspective.
Chapter 14. Reason and Knowledge.
Chapter 15. Reason, Knowledge and Emotion.
Chapter 16. Logic, Evolution, Language and Reason
Chapter 17. Logic, Method and Knowledge.
Chapter 18. Classifying and Justifying Inference Rules
Chapter 19. Philosophy and Knowledge.
Part IV: Rules of Discovery.
Chapter 20. Induction and Analogy.
hapter 21. Other Rules of Discovery.
Chapter 22. Conclusion.
References.
Name Index
Subject Index.