Math is Everywhere PDF
Preview Math is Everywhere
MATH IS EVERYWHERE! EXPLORE AND DISCOVER IT! Fifth Edition Custom Edition for St. Petersburg College James J. Rutledge Illustrations by Joyce T. Rutledge Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc. Cover Art: Text illustrated by Joyce T. Rutledge All rights reserved. Permission in writing must be obtained from the publisher before any part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system. All trademarks, service marks, registered trademarks, and registered service marks are the property of their respective owners and are used herein for identification purposes only. Pearson Learning Solutions, 501 Boylston Street, Suite 900, Boston, MA 02116 A Pearson Education Company www.pearsoned.com Printed in the United States of America 1 2 3 4 5 6 7 8 9 10 XXXX 17 16 15 14 13 12 000200010271627154 CW ISBN 10: 1-256-67707-8 ISBN 13:978-1-256-67707-9 Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc. To Joyce, Justin and Nathan and To all of my students and colleagues who have inspired and encouraged me along the way J. R. Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc. Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc. Math Is Everywhere! Explore and Discover It! Math Is Everywhere! Explore and Discover It! Fifth Edition Table of Contents Introduction and Welcome: To Know the End from the Beginning… v Chapter 1: Reasoning and Resources: Tools for Life 1 1.0 Introduction and Objectives 1 1.1 Analytical Reasoning: A Tool for Life 3 Project: Pascal’s Famous Triangle 6 1.2 Math Classics and Applied Reasoning 8 Project: Guards and Prisoners 19 Project: Cross-number Puzzle 20 1.3 Resources for the Present and the Future 22 Project: MERLOT and You 26 Chapter 2: Patterns and Reasoning: Fun with Math! 29 2.0 Introduction and Objectives 29 2.1 Deductive and Inductive Reasoning 32 Project: A Riddling Good Time 46 2.2 Pattern Recognition: Searching for Connections 49 Project: The Curious Date: 7-14-98 62 Project: Another Curious Date: 10-1-01 63 2.3 The nth Term: The Power of Generalization 65 Project: Sequence Creations 81 Project: Generalization—A Powerful Tool 82 2.4 Logical Thinking and Reasoning Backwards 85 Project: Puzzle Constructions 99 2.5 Magic Squares: Sum Fun! 103 Project: Magic Squares 116 Project: Magic Square Extensions 117 Chapter 3: Math from Other Times and Places: Historical Investigations 121 3.0 Introduction and Objectives 121 3.1 The Greeks: Students and Investigators 123 v Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc. Math Is Everywhere! Explore and Discover It! Project: Polygonal Numbers—A Geometric View 126 3.2 Pascal’s Amazing Triangle: Simple yet Profound 128 Project: Pascal’s Triangle 129 3.3 Number Systems through the Ages: Stylistic and Diverse 130 Project: The Abacus 137 Project: Numeration in Other Cultures 138 Chapter 4: Number Bases: Surprising Versatility 139 4.0 Introduction and Objectives 139 4.1 Understanding Other Number Bases: Places of Value 141 Project: The Banker’s Dilemma 152 4.2 The Binary System: Secret Language of Computers 156 Project: Chinese Trigrams and Binary Numbers 158 Project: The ASCII Code 160 Project: Course Logo: A Hidden Message 166 4.3 Number Base Applications: More Fun with Math! 167 Project: Hexadecimals 172 Chapter 5: Modulus Arithmetic and Its Many Uses 173 5.0 Introduction and Objectives 173 5.1 Clock Systems: The Cycles of Life 175 Project: Perpetual Calendar 180 5.2 The Modulus in Action: Check Digits and Error Detection 185 Project: ISBN Numbers and Modulus Arithmetic 190 Project: ISMN Numbers and Modulus Arithmetic 193 5.3 Cryptography: The Mathematics of Privacy 195 Project: Cryptograms—A Popular Pastime 207 Project: Cryptoquotes—Another Favorite 207 Chapter 6: Mathematics and Music: Inseparable Partners 209 6.0 Introduction and Objectives 209 6.1 The Nature of Sound and Musical Scales: Good Vibrations 211 Project: Creating Good Vibrations 223 Project: Famous Math Quotes 224 6.2 The Mathematics of Stringed Instruments: Structured Harmony 225 Project: Guitar Analysis 227 6.3 Digital Music and CD’s: Applied Mathematics 234 Project: Digital Music and Mathematics 236 vi Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc. Math Is Everywhere! Explore and Discover It! Chapter 7: Mathematics in Art, Architecture and Nature 239 7.0 Introduction and Objectives 239 7.1 Mathematical Perspective in Art: A Renaissance Breakthrough 241 Project: Mathematical Perspective 245 7.2 Symmetry and Tilings: Mathematical Beauty and Artistry 248 Project: Tilings in your Home 253 Project: Symmetry and Tilings 254 Project: The Mathematical Art of M.C. Escher 255 7.3 Mathematics in Architecture and Nature: The Golden Section and Fibonacci 256 Project: The Amazing Rabbit Population 260 Project: Golden Rectangles in your Home 261 Project: Fibonacci Numbers in Nature and the Arts 262 Project: Logarithmic Spirals—Seashell Design 263 7.4 Long-term Projects 266 Project: Webliography Report 267 Project: Term Report 268 Project: Stock Market Investment Report 270 Chapter 8: Fractals: New Structures in Mathematics 273 8.0 Introduction and Objectives 273 8.1 Mathematical Fractals: A Natural Geometry 275 Project: Introduction to Fractals 281 8.2 Fractal Applications 284 Project: Fractals in Nature 291 Project: Fractal Music 292 Project: Fractal Art 292 8.3 Famous Triangles: Sierpinski Meets Pascal 293 Project: Triangle Connections 296 Chapter 9: Linear Relationships: Straight as an Arrow 299 9.0 Introduction and Objectives 299 9.1 Mathematical Relationships and Functions: “Vary-ables” in Action 301 Project: The Shape of Daylight 317 9.2 Linear Functions: A Deeper Look 318 9.3 Linear Models: Analytic and Predictive 336 Project: How Does your Lawn Grow? 346 Project: How Does your Garden Grow? 347 vii Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc. Math Is Everywhere! Explore and Discover It! Chapter 10: Exponential Growth: Drama and Suspense 349 10.0 Introduction and Objectives 349 10.1 Doubling Power: An Amazing Phenomenon 351 10.2 The Exponential Function: A Deeper Look 358 Project: World Population Growth 367 10.3 Exponential Models and Applications 368 Project: U.S. Population Growth 371 Project: The Fastest Growing State in the U.S.? 372 Project: Population Growth in Florida 372 Chapter 11: Financial Planning: Mathematical Secrets to Acquiring Wealth 373 11.0 Introduction and Objectives 373 11.1 Compound Interest: Strategies for Wealth 375 Project: The Long-Term Results of Compound Interest 386 11.2 Savings Plans: Don’t Leave Home Without One! 389 Project: Intro to Savings and Investment 391 11.3 Stocks, Bonds and Mutual Funds 392 Project: Intro to Stocks, Bonds and Mutual Funds 394 Project: Investment Strategies 395 Project: A True and Amazing Story 396 Project: Stock Market Investment Report 397 11.4 Home Mortgages: Mathematical Revelations 399 Project: The All-Powerful Interest Rate 409 11.5 Credit Card Economics 412 Project: Credit Reports and Ratings: An Inside Look 414 Project: The Truth about Credit Card Debt 415 ******************** Appendices 421 Appendix A: Helps and Hints for Exercises and Projects 423 Appendix B: Cross-number Puzzle Terminology 447 Appendix C: Guide to Correlation Coefficients 451 Appendix D: Fractal Structures: Italian Parsley 455 ******************** viii Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc. Math Is Everywhere! Explore and Discover It! Introduction and Welcome: To Know the End from the Beginning… Introduction and Welcome: To Know the End from the Beginning… Introduction Welcome to Math Is Everywhere! Explore and Discover It!, a unique, project-based mathematics textbook and course of study for college students, particularly those who are Liberal Arts majors, and for anyone interested in mathematics and its relevance and application in today’s world. While written for entry-level college students in general, this text is especially suited for those who might be math-avoiders or math-phobic. It is also suited for those who may become elementary, middle or high school mathematics teachers; the content has much to offer in the way of mathematical ideas and resources for future educators. If you have ever felt that math was a dry and boring subject and wondered, “Why do I have to learn this?” or “When will I ever use this?”, then this textbook is for you! You’ll soon discover that mathematics has many fascinating and practical connections to music, art, architecture, nature, sports, finance, food, and much more, and I’m confident that you will thoroughly enjoy this textbook and course of study. In the Beginning This text was written to engage students in active learning and to reveal the beauty, practicality and pervasiveness of math in our daily lives. Math Is Everywhere! provides an effective means by which students can overcome their negative associations with math and find empowerment in their own analytical reasoning and critical thinking abilities. The text conveys a sense of enthusiasm, offers encouragement for success, and provides a wealth of opportunities for students to become engaged in mathematics in interesting and enjoyable ways. Goals and Objectives Math Is Everywhere! is designed around the following seven goals: to engage students in active learning through the use of projects and activities to demonstrate the beauty, practicality and pervasiveness of math in our daily lives to lead students into a new and refreshing relationship with mathematics to alleviate student math anxiety to enable students to develop their analytical reasoning and critical thinking skills to promote technological skills to encourage students to become lifelong learners of mathematics ix Math is Everywhere, Fifth Custom Edition, by Jim Rutledge. Published by Pearson Learning Solutions. Copyright ' 2012 by Pearson Education, Inc.
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