Hidden Harmonies: The Lives and Times of the Pythagorean Theorem

( 2 )

Overview

A squared plus b squared equals c squared. It sounds simple, doesn?t it? Yet this familiar expression opens a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons?not to mention the elusive ...

See more details below
Paperback
$16.03
BN.com price
(Save 10%)$18.00 List Price

Pick Up In Store

Reserve and pick up in 60 minutes at your local store

Other sellers (Paperback)
  • All (27) from $1.99   
  • New (16) from $2.73   
  • Used (11) from $1.99   
Hidden Harmonies: The Lives and Times of the Pythagorean Theorem

Available on NOOK devices and apps  
  • NOOK Devices
  • Samsung Galaxy Tab 4 NOOK
  • NOOK HD/HD+ Tablet
  • NOOK
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac
  • NOOK for Web

Want a NOOK? Explore Now

NOOK Book (eBook)
$10.49
BN.com price
(Save 30%)$14.99 List Price

Overview

A squared plus b squared equals c squared. It sounds simple, doesn’t it? Yet this familiar expression opens a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons—not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name. As in the authors’ bestselling The Nothing That Is and Chances Are..., the excitement of mathematics leaps from the pages of Hidden Harmonies.

Read More Show Less

Editorial Reviews

Publishers Weekly
The Kaplans (Out of the Labyrinth) collaborate for a fourth time on this historical and mathematical examination of the Pythagorean Theorem (a2+b2=c2). Going well beyond the typical school treatment of the subject, the Kaplans use proofs and diagrams to demonstrate that "the Pythagorean Theorem...holds even when the most art nouveau shapes flourish on a right triangle's hypotenuse, along with shapes similar to it on the legs. They can, if you wish, be as lacy as your great-grandmother's antimacassars, so long as they have areas." People throughout the ages, from Leonardo da Vinci to President James A. Garfield, have found multiple methods for constructing proofs of this famous and useful theorem, and the Kaplans provide many of them along with background information and context. The Kaplans are wonderfully chatty hosts—"The begottens and begets of mathematics never end—not because of some dry combinatorial play, but because curiosity always seeks to justify the peculiar, and imagination to shape a deeper unity"—often asking questions to inspire thinking. Some readers may wish for a more direct approach, but the Kaplans combine math history and theory with humor, compelling tidbits, and helpful equations (along with an analysis of tangrams) to create an entertaining and stimulating book for the mathematically inclined. Illus. (Jan.)
From the Publisher
“Beauty, intrigue, paradox and surprise. Mathematics, in its true essence, is a deeply organic and intensely human enterprise and Bob and Ellen Kaplan are the masters of reveling in its delight and elucidating its richness. Hidden Harmonies is a stunning book, taking the most classic theorem in mathematics and exposing its story, its human story, for what it really is: true poetry.”—James Tanton, PhD, author and educator, founding director of the St. Mark’s Institute of Mathematics

“…The authors succeed in explaining the arcane aspects of the subject, and they are diligent in situating the Pythagorean theorem within the historical rise of mathematics. That they revel in the subject is clear…”Wall Street Journal

“Showing the theorem’s endless versatility, the Kaplans and their logic- and symbol-permeated text will engage those who delight in doing the math.”—Booklist

“Enthusiasm and wit make the material appealing even to readers who aren't mathematicians … inspired.”—Kirkus

 

“The book possesses an alluring lyricism and a good sense of humor, and it’s often as fun to be around…”—Anthony Doerr, Boston Globe

 

“The Kaplans have given us a wonderful, fun, and entertaining math book.”Library Journal

Library Journal
The Kaplans (The Nothing That Is: A Natural History of Zero) have brought to life the Pythagorean theorem. They trace the development and treatment of this fundamental geometrical relationship from ancient times through the Middle Ages to the modern era. It is not an exaggeration to say that the Pythagorean theorem forms the basis of most of the mathematical expressions of our physical world. It is rare that a mathematical topic is presented in a manner that is light and entertaining and yet has depth and richness. The book is chock-full of geometrical illustrations along with ample equations and a few portrait images to accompany the abundant biographical information on mathematicians' whose proofs they consider. VERDICT Readers with some mathematical background will appreciate the geometrical and logical nuances, but even those less proficient in mathematics will grasp the essentials. Folks who love and live mathematics (and those in science and technology) will thoroughly enjoy this book. The Kaplans have given us a wonderful, fun, and entertaining math book.—Margaret Dominy, Drexel Univ. Lib., Philadelphia
Kirkus Reviews

Popular math writers Robert and Ellen Kaplan (Out of the Labyrinth: Setting Mathematics Free, 2007, etc.) examine the far-reaching, and at times exotic,applications ofthe familiar theorem.

With its origin traced back as far as ancient Babylon, the properties inherent in the Pythagorean Theorem (Asquared + B squared = Csquared) have had myriad implications both pedestrian and profound, from basic land-area assessment to architecture to physics. Thousands of people have worked out Pythagorean proofs, including President James Garfield while he was in the House of Representatives—further testament to both its alluringnature and astonishing versatility. (Interestingly, Pythagoras is not believed to have formulated the theorem named after him, which only adds to the mystique.) From a modern perspective, everything from differential calculus to astronomy utilizes the theorem's principles, and it has even been proven to apply to figures inmultiple dimensions,up to infinity, and to hint at the intriguing realm of irrational numbers.The authors, whose enthusiasm and wit make the material appealing even to readers who aren't mathematicians, write that such inspired deductions provide "the giddy sort of sensation that often leads people into mathematics: grasping something infinite via abstraction (as children love dinosaurs, because they are both very big and not quite real)." The book contains a healthy number of equations and proofs, some of which are intimidating, but the authors maintain an engaging plainspoken narrative peppered with references to, among many others, Shakespeare, Jefferson, Freud, Einstein andDescartes. It's clear that this theorem continues to play an important role in math and science, that the human capacity for theoretical exploration remains unabated and that our "curiosity always seeks to justify the peculiar, and imagination to shape a deeper unity." As such, this engaginghistory ofthe elegantly simple theorem provides readers with much more to ponder than just the mathematical.

May not be widely accessible, but for the right reader, anenthralling exploration of this ancient rule of ratios.

Read More Show Less

Product Details

  • ISBN-13: 9781608193981
  • Publisher: Bloomsbury USA
  • Publication date: 9/4/2012
  • Edition number: 1
  • Pages: 304
  • Sales rank: 936,348
  • Product dimensions: 8.10 (w) x 5.50 (h) x 0.90 (d)

Meet the Author

Robert and Ellen Kaplan have taught mathematics to people from six to sixty, at leading independent schools and, most recently, at Harvard University. Robert Kaplan is the author of the bestselling The Nothing That Is: A Natural History of Zero, which has been translated into 10 languages, and together they wrote The Art of the Infinite and Out of the Labyrinth. Ellen Kaplan is also co-author of Chances Are: Adventures in Probability and Bozo Sapiens: Why to Err Is Human, co-written with her son Michael Kaplan. They live in Southampton, Massachusetts.

Read More Show Less

Table of Contents

An Outlook on Insights xi

Chapter 1 The Mathematician as Demigod 1

Chapter 2 Desert Virtuosi 6

Chapter 3 Through the Veil 44

Chapter 4 Rebuilding the Cosmos 63

Chapter 5 Touching the Bronze Sky 81

Chapter 6 Exuberant Life 138

Chapter 7 Number Emerges from Shape 177

Chapter 8 Living at the Limit 192

Chapter 9 The Deep Point of the Dream 224

Chapter 10 Magic Casements 254

Afterword Reaching Ihrough-or Past-History? 262

Acknowledgments 265

Notes 267

Selected Bibliography 277

Index 281

Read More Show Less

Customer Reviews

Average Rating 5
( 2 )
Rating Distribution

5 Star

(2)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously
Sort by: Showing all of 2 Customer Reviews
  • Posted September 24, 2011

    Well worthwhile

    For anyone interested in Mathematics, at sny level, the Pythagorian Theorem is ubiquitous, to say the least. I was surprised to learn that Pythagoras was a Johnny-come-lately in the right triangle game. I was also surprised at the story of a Cleveland Geometry teacher who devised about 300 different proofs for the Theorem. He taught at a Cleveland high school at the turn of the century. Now, a century later, I'm teaching Geometry at the same school. The book is loaded with surprises. By all means - read it

    2 out of 2 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
  • Posted May 23, 2011

    Right-brainers take heed

    Very well written. Quick and fascinating read

    Was this review helpful? Yes  No   Report this review
Sort by: Showing all of 2 Customer Reviews

If you find inappropriate content, please report it to Barnes & Noble
Why is this product inappropriate?
Comments (optional)