## Hidden Harmonies: The Lives and Times of the Pythagorean TheoremA squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors 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.How can a theorem have more than one proof? Why does this one have more than two hundred-or is it four thousand? The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning-the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples. Like the authors' bestselling The Nothing That Is and Chances Are . . .-hailed as "erudite and witty," "magnificent," and "exhilarating"-Hidden Harmonies makes the excitement of mathematics palpable. |

### What people are saying - Write a review

#### LibraryThing Review

User Review - fpagan - LibraryThingMany a reader, I think, would find this volume's writing to be too clever and erudite for its own good. A more straightforward popularization on the Pythagorean Theorem and related mathematics, such ... Read full review

#### HIDDEN HARMONIES: The Lives and Times of the Pythagorean Theorem

User Review - Jane Doe - KirkusPopular math writers Robert and Ellen Kaplan (Out of the Labyrinth: Setting Mathematics Free, 2007, etc.) examine the far-reaching, and at times exotic, applications of the familiar theorem.With its ... Read full review

### Contents

CHAPTER | 6 |

CHAPTER THREE | 44 |

CHAPTER FOUR | 63 |

CHAPTER FIVE | 81 |

CHAPTER | 138 |

CHAPTER EIGHT | 192 |

CHAPTER NINE | 224 |

CHAPTER | 254 |

AFTERWORD Reaching Throughor PastHistory? | 262 |

275 | |

### Other editions - View all

Hidden Harmonies: The Lives and Times of the Pythagorean Theorem Ellen Kaplan,Robert Kaplan Limited preview - 2011 |

Hidden Harmonies: The Lives and Times of the Pythagorean Theorem Ellen Kaplan,Robert Kaplan No preview available - 2012 |

### Common terms and phrases

abstract algebra ancient angle sum appendix approximation Barry Mazur Burkert called Chapter circle congruent Construct cosh diagonal diagram Dijkstra dimensions Edsger Wybe Dijkstra equal equation Euclid Euclidean example figure finite functions geometry gives gnomon Greek Guido’s Hence Here’s Hippasus hyperbolic hypotenuse ifwe ifyou imagination induction infinite inner product isosceles law of cosines Lemma length Liu Hui look Loomis math mathematician mathematics measure mind multiplying n-dimensional natural numbers ofthe squares Old Babylonian Parallel Postulate parallelogram path pebbles perpendicular plane Plimpton 322 polygons postulates problem proof prove pseudosphere Pythagoras Pythagorean Insight Pythagorean Theorem Pythagorean triples rational rectangle relatively prime right angle right triangle Robson segments shape side-length sides similar solutions space sphere step tablet tells Thabit thagorean thought tion triangle’s trigonometry vectors What’s whole numbers