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Magnificent Mistakes in Mathematics

Author: Alfred S. Posamentier

Publisher: Prometheus Books

Published: 2013-08-13

Total Pages: 298

ISBN-13: 1616147482

Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results. Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

Magnificent Mistakes in Mathematics

Author: Alfred S. Posamentier

Publisher:

Published: 2013

Total Pages: 298

ISBN-13: 1616147474

DOWNLOAD EBOOK →

In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places.This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. Veteran math educators Alfred S. Posamentier and Ingmar Lehmann demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. For example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid--that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd--but enlightening--results.Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

Challenging Problems in Algebra

Author: Alfred S. Posamentier

Publisher: Courier Corporation

Published: 2012-05-04

Total Pages: 288

ISBN-13: 0486131548

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Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.

Mathematics Entertainment For The Millions

Author: Alfred S Posamentier

Publisher: World Scientific

Published: 2020-07-21

Total Pages: 304

ISBN-13: 9811219303

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'The physical form of this new title is pleasing, including good paper, readable font, and durable binding … The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership.Summing Up: Recommended. General readers.'CHOICEThis book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations.The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level.Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics — to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics — something most general readers will not initially find possible, but we hope will be an end product of this book.

Solving Problems In Our Spatial World

Author: Guenter Maresch

Publisher: World Scientific

Published: 2019-06-20

Total Pages: 381

ISBN-13: 9813278056

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'The reference list is excellent. This is a worthwhile (though 'niche') book that will be attractive to a particular sector of the general reading public interested in mathematical riddles and puzzles. Professional educators might well employ it in integrated learning settings. Summing Up: Recommended. All readers.'CHOICEImmerse yourself in the fascinating world of geometry and spatial ability — either individually or in small groups, either as challenges or play problems! Here are four reasons why you should work with this book:This book offers a very unique opportunity to enhance your spatial ability, your mathematical competence, and your logical thinking. The authors arranged 45 problems — including more than 120 tasks — in a well-balanced order, which have been tested with a variety of populations.

Math Charmers

Author: Alfred S. Posamentier

Publisher: Prometheus Books

Published: 2011-04-26

Total Pages: 301

ISBN-13: 1615921729

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Readers are invited to have fun with math in this reader-friendly volume--theideal book for adults looking for a way to turn their kids on to an importantsubject. Illustrations throughout.

How Not to Be Wrong

Author: Jordan Ellenberg

Publisher: Penguin

Published: 2015-05-26

Total Pages: 482

ISBN-13: 0143127535

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“Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

Our Mathematical Universe

Author: Max Tegmark

Publisher: Vintage

Published: 2015-02-03

Total Pages: 434

ISBN-13: 0307744256

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Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.

Humble Pi

Author: Matt Parker

Publisher: Penguin

Published: 2021-01-19

Total Pages: 337

ISBN-13: 0593084691

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#1 INTERNATIONAL BESTSELLER AN ADAM SAVAGE BOOK CLUB PICK The book-length answer to anyone who ever put their hand up in math class and asked, “When am I ever going to use this in the real world?” “Fun, informative, and relentlessly entertaining, Humble Pi is a charming and very readable guide to some of humanity's all-time greatest miscalculations—that also gives you permission to feel a little better about some of your own mistakes.” —Ryan North, author of How to Invent Everything Our whole world is built on math, from the code running a website to the equations enabling the design of skyscrapers and bridges. Most of the time this math works quietly behind the scenes . . . until it doesn’t. All sorts of seemingly innocuous mathematical mistakes can have significant consequences. Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean. Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.

Strategy Games To Enhance Problem-solving Ability In Mathematics

Author: Alfred S Posamentier

Publisher: World Scientific

Published: 2016-11-11

Total Pages: 136

ISBN-13: 9813146362

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Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.