# Pythagoras' Revenge: A Mathematical Mystery

By Arturo Sangalli | Go to book overview

Appendix 4
A Simple Visual Proof of the
Pythagorean Theorem

The area of a square of side a + b is (a + b)2 or a2 + b2 + 2ab (I).

On the other hand, if the interior of the square is divided up into a square of side c and four right-angled triangles of sides a, b as shown below, its area equals the sum of the areas of these five figures, that is c2 + 4(ab/2) or c2 + 2ab (II).

Since the expressions (I) and (II) represent the same area, we have

a2 + b2 + 2ab = c2 + 2ab, which implies

a2 + b2 = c2

-177-

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Pythagoras' Revenge: A Mathematical Mystery

• Title Page iii
• Contents v
• Preface ix
• List of Main Characters (Chapter in Which They Are Introduced) xi
• Prologue xiii
• Part I- A Time Capsule? 1
• Chapter 1- The Fifteen Puzzle 3
• Chapter 2- The Impossible Manuscript 10
• Chapter 3- Game over 19
• Chapter 4- A Trip to London 25
• Chapter 5- A Letter from the Past 32
• Chapter 6- Found and Lost 38
• Chapter 7- A Death in the Family 46
• Part II- An Extraordinarily Gifted Man 51
• Chapter 8- The Mission 53
• Chapter 9- Norton Thorp 63
• Chapter 10- Random Numbers 69
• Chapter 11- Randomness Everywhere 76
• Chapter 12- Vanished 82
• Part III- A Sect of Neo­ Pythagoreans 83
• Chapter 13- The Mandate 85
• Chapter 14- The Beacon 87
• Chapter 15- The Team 98
• Chapter 16- The Hunt 106
• Chapter 17- The Symbol of the Serpent 115
• Chapter 18- A Professional Job 122
• Chapter 19- with a Little Help from Your Sister 126
• Part IV- Pythagoras' Mission 137
• Chapter 21- Kidnapped 152
• Chapter 22- The Last Piece of the Puzzle 158
• Epilogue 169
• Appendix 1- Jule's Solution 171
• Appendix 2- Infinitely Many Primes 173
• Appendix 3- Random Sequences 175
• Appendix 4- A Simple Visual Proof of the Pythagorean Theorem 177
• Appendix 5- Perfect and Figured Numbers 178
• Notes, Credits, and Bibliographical Sources 181
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