Cover image for The mathematics of everyday life / Alfred S. Posamentier and Christian Spreitzer.
Title:
The mathematics of everyday life / Alfred S. Posamentier and Christian Spreitzer.
ISBN:
9781633883871
Publication Information:
Amherst, New York : Prometheus Books, 2018.

©2018
Physical Description:
424 pages : 24 cm
General Note:
Includes index.
Contents:
Historical high points in the development of mathematical applications -- Mathematics in our everyday lives : arithmetic shortcuts and thinking mathematically -- Mathematical appearances and applications in everyday life problems -- Probability,games and gambling -- Sports and games : explained mathematically -- The world and its nature -- Mathematics appearances in art and architecture -- The technology around us : from a mathematical perspective.
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Summary

Summary

If you think of mathematics as a series of pointless classroom exercises without much relevance to real life, this book will change your mind. As the authors show, math is deeply embedded in almost every aspect of daily life--from managing your personal finances, making consumer purchases, and sharpening your computational skills, to learning to apply mathematical concepts that will give you a better grasp of both ordinary and extraordinary events and help you better appreciate the world we live in. With some basic geometry under your belt, you'll discover that there is an optimal point on a soccer field from which to shoot a goal. And you'll be more clever with the gears of a bike. If you like to play cards or go to the casino, knowing something about probability will give you an edge. You'll also have an enhanced understanding of the "whispering effect" inside the Capitol rotunda, why a car's headlights are so bright, and even why sewer covers are round.


Author Notes

After reading this entertaining and instructive book, you'll come away with a whole new awareness of how elegantly mathematics explains everyday experiences and observations--from present day items to classical art and architecture.


Excerpts

Excerpts

Introduction We hear so often that mathematics is important for us to better appreciatethe world around us. This is the book that will guide you througha wide variety of aspects of our world that are accompanied by mathematical explanations. Unfortunately, because of restricted curriculum guidelines, your teachers and school probably did not have the time to navigate the many excursions that we will be presenting here. Had they been able to enrich mathematics instruction through these many applications, your math instruction would have been much more enjoyable. Teachers are strictly directed by curriculum guidelines to cover topics considered essential foundation blocks for further study in mathematics as well as the other STEM fields. This is compounded even more so in many schools where teachers are rated by the scores that their students achieve on standardized tests. Hence, there is a lot of "teaching to the test" and very little beyond that. In this book, we plan to dispel the very popular notion that mathematics is tedious and boring. We will be presenting a host of topics and ideas you are unlikely to have encountered during your school instruction, and they will give you a true feeling of how mathematics is a part of our everyday lives and how it can be used to explain many of the concepts we experience, the things we see, the decisions we make, and the overall understanding we have of the world around us. Most people experience mathematics in a formal sense during their school years. All too often, mathematics is presented as a collection of mechanical techniques that supposedly allow the learner to apply these methods and concepts to a variety of encounters in everyday life. But the lifestyles and interests of the general populace vary broadly. Compound that with the lack of applications in the curriculum, and the average person is left with the feeling that he or she learns mathematics because it had to be learned and not because it is useful. In this book, we hope to convince you not only that mathematics is useful, but also that it can help us explain many things in everyday life that we tend to take for granted--and in unexpected ways. There are people who feel that they can explain the world through mathematics. Oftentimes there may be a bit of a "stretch" in such explanations. Yet there are numerous parts of our experiential world that are based on mathematical concepts and principles. These can be appreciated in a variety of forms of art, architecture, nature, and finance; further, the daily aspects of our culture and lifestyles have mathematical explanations, or even mathematical origins. Most people are unaware as they confront these things that simple mathematics is being applied or can be used to better explain what is being observed. As mentioned above, mathematical applications can be found in art and architecture, where the proportions of pictures, their subjects, and the nature of the structures themselves can be explained with well-established mathematical relationships. The golden ratio, which shows its tested beauty on the dimensions of the golden rectangle, is used throughout art and architecture. The structures that have for centuries become icons in our society--such as famous cathedrals, the Parthenon, the pyramids in Egypt--and other notable structures, even those built in modern times--such as the Headquarters of the United Nations in New York--all exhibit the beautiful golden ratio. Additionally, for paintings to convey proper depth perception, lines of perspectivity also must come into play; we can see this in Leonardo da Vinci's famous The Last Supper mural in Milan, Italy, for example. Through their drawings and paintings, well-known artists have demonstrated their awareness of mathematical concepts. Notably among these is the famous German artist Albrecht Dürer, who studied Leonardo's techniques and used them in some of his drawings. He also showed a keen awareness of mathematics in his 1514 etching Melencolia I , in which he included an incredibly rich magic square that has many prop-erties beyond those of normal magic squares. We hope to give you the tools you need to appreciate art and architecture from a mathematical standpoint, as well as an aesthetic one. Perhaps the most ubiquitous numbers in mathematics are the Fibonacci numbers, which continuously arise in just about every aspect of our lives. For example, in nature the numbers of spirals on pine cones and pineapples are always Fibonacci numbers, as is the arrangement of the branches on a pear tree. You'll have to read on to learn about even more amazing appearances and applications of the Fibonacci numbers. (By the way, the Fibonacci numbers can also generate the golden ratio!) Beyond art and the natural world, there are also unexpected, curious mathematical explanations for understanding excellence in sports. For example, you can use very simple high-school geometry to determine the optimal point along the sideline of a soccer field from which to shoot a goal. You can also use simple geometry in billiards to easily determine the point at which to hit a ball with the cue so that it hits a cushion and ricochets onto another cushion or ball. You might not think about this when playing a game of billiards for fun with your friends, but this is just another example of how math is all around you. As you know, we all do lots of calculating and estimating in the course of our everyday lives. But you will be surprised, and perhaps entertained, by the many shortcuts and unusual relationships that can be used to make these tasks almost trivial, such as when converting miles to and from kilometers. We will present a variety of useful shopping shortcuts, investment insights, even how best to wrap a present! Mathematics can help you navigate the globe and even appreciate and understand rainbows and the other curves that we encounter. For instance, when you travel along a road with timed traffic lights, mathematics can explain how this is done. Have you ever wondered why all sewer covers are round? That, too, will be explained. There are curves that enable us to have whispering galleries, and curves that hold up bridges. All of these are special properties that can be explained very easily through elementary mathematics. The field of probability allows us insight into some unusual aspects of reality, too. It is clearly to a gambler's advantage to understand concepts of probability, for oftentimes a correct assessment of a wagering situation can be quite counterintuitive. There are game shows on television, most notably Let's Make a Deal , that have been a hot topic of controversy regarding how to determine the best strategy to win the game. Probability can also affect your worldview, particularly when you are reading a newspaper and journalists enthusiastically offer statistical evidence to support a position; at this point, knowledge of probability concepts can be helpful not only to understand the presented material but also to criticize it intelligently. We hope to enlighten you in this regard. We will also provide some curious insights into the card game of poker. As you will see, mathematical problem-solving strategies are often used in everyday life. For example, using extremes to solve certain problems can be very effective not only in mathematics, but also with issues we face regularly. When confronted with a decision to be made, we say to ourselves, "Well, in the worst-case scenario, such and such would be the case." This allows us to move ahead with a sensible procedure for dealing with the situation at hand. Mathematical problem-solving strategies can guide us in the way we think about common, everyday decisions to be made. These are just a few of the plethora of mathematical applications in our everyday lives. Often, we are not even aware that mathematics can explain and facilitate an understanding of what we see and how we can best deal with these situations. The mathematical concepts we consider in this book will require nothing more than a recollection of what you had been taught up to the tenth grade in high school. Join us now as we begin our journey through an investigation of a wealth of topics that either depend on mathematics or can use mathematics to explain their functioning, or, perhaps, even allow us to appreciate the world around us in an enhanced, sophisticated fashion because now many things we may have just accepted without question will become more meaningful. Excerpted from The Mathematics of Everyday Life by Alfred S. Posamentier, Christian Spreitzer All rights reserved by the original copyright owners. Excerpts are provided for display purposes only and may not be reproduced, reprinted or distributed without the written permission of the publisher.

Table of Contents

Introductionp. 11
Chapter 1 Historical High Points In The Development of Mathematical Applicationsp. 15
The Origin of Our Number Symbolsp. 15
The Most Important Number in Mathematicsp. 17
The Famous Fibonacci Numbersp. 20
Arithmetic in Ancient Egyptp. 21
Where the Terms Related to Our Clock Evolvep. 28
A Minute History of Timekeepingp. 28
Babylonian Mathematics and the Sexagesimal Systemp. 29
Babylonian Minutes and Seconds Have Survived to This Dayp. 33
Roman Numerals Are Everywhere around Usp. 34
Mathematics on the Calendarp. 39
How We Overlook Our Calendarp. 48
Chapter 2 Mathematics In Our Everyday Lives-Arithmetic Shortcuts and Thinking Mathematicallyp. 53
Arithmetic with the Numbers 9 and 11p. 54
How 9s Can Check Your Arithmeticp. 60
Rules for Divisibilityp. 62
A Quick Method to Multiply by Factors of Powers of 10p. 68
Arithmetic with Numbers of Terminal Digit 5p. 69
Multiplying Two-Digit Numbers Less Than 20p. 71
Mental Arithmetic Can Be More Challenging-but Useful!p. 73
Arithmetic with Logical Thinkingp. 74
Using the Fibonacci Numbers to Convert Kilometers to and from Milesp. 75
Thinking "Outside the Box"p. 79
Solving Problems by Considering Extremesp. 82
The Working-Backward Strategy in Problem Solvingp. 86
Chapter 3 Mathematical Appearances and Applications In Everyday-Life Problemsp. 93
Shopping with Mathematical Supportp. 93
Successive Percentagesp. 94
Raising Interest!p. 100
The Rule of 72p. 104
Paper Sizes and the Root of All ISOp. 106
Comparing Areas and Perimetersp. 110
Mathematics in Home Constructionp. 113
The Perfect Manhole Coverp. 117
Design Your Own Coffee-Cup Sleeve!p. 124
How to Optimally Wrap a Presentp. 128
Chapter 4 Probability, Games, and Gamblingp. 135
Friday the Thirteenth!p. 135
Unexpected Birthday Matchesp. 137
Selecting Clothesp. 141
Playing Cards, a Counterintuitive Probabilityp. 142
Mathematics in Pokerp. 144
Mathematical Logic of Tic-Tac-Toep. 150
The Monty Hall Problemp. 154
Business Applicationsp. 158
Mathematics of Life Insurancep. 163
The Most Misunderstood Averagep. 168
What We Need to Know about Averagesp. 170
Comparing Measures of Central Tendencyp. 172
Chapter 5 Sports and Games-Explained Mathematicallyp. 181
The Best Angle to Throw a Ballp. 181
Optimizing Your Shot at Soccerp. 187
A Game of Anglesp. 192
Playing Billiards Cleverlyp. 201
Mathematics on a Bicyclep. 206
The Spirograph Toyp. 212
Chapter 6 The World and Its Naturep. 225
Measures of and on the Earthp. 225
Navigating the Globep. 229
What Is Relativity?p. 232
Coloring a Mapp. 233
Crossing Bridgesp. 237
Mathematics in Naturep. 243
The Male Bee's Family Treep. 244
Fibonacci Numbers in the Plant Worldp. 246
The Pine Cone and Othersp. 247
Leaf Arrangement-Phyllotaxisp. 251
The Fibonacci Numbers on the Human Bodyp. 255
The Geometry of Rainbowsp. 258
Chapter 7 Appearances of Mathematics In Art and Architecturep. 275
Golden Ratio Sightingsp. 276
Displaying a Watchp. 281
Applications in Artp. 284
Perspectivity in Artp. 296
Numbers in Artp. 305
Viewing a Statue Optimallyp. 309
The Most Overlooked Curvep. 312
The One-Sided Belt-the Möbius Stripp. 315
Chapter 8 The Technology Around Us-From A Mathematical Perspectivep. 319
A Fascination with the Clockp. 319
The Mathematics of Paper Foldingp. 322
Building a Skewed Towerp. 328
Whispering Galleriesp. 334
Looking inside a Flashlightp. 345
Coffee with Causticsp. 351
Green Traffic Lights All the Wayp. 356
Safety in Numbersp. 365
The ISBN Systemp. 376
How the Global Positioning System (GPS) Worksp. 381
Acknowledgmentsp. 391
Notesp. 393
Indexp. 401