The Amazing Number Pi Dev Gualtieri http://www.tikalonpress.com Copyright © 2013 D.M. Gualtieri All rights reserved. ISBN: 978-0-9853325-8-7 CONTENTS Table of Contents Author's Foreword...............................................v Pi Digits 1-24......................................................1 History................................................................1 Pi as a Number...................................................7 Calculating Pi....................................................22 Pi Digits 25-49..................................................25 Pi Digits 50-74..................................................50 Feats of Strength..............................................59 Calculating with Pi............................................63 Miscellaneous Facts..........................................70 Pi Digits 75-100................................................75 Mnemonics.......................................................93 Pi Approximations.............................................97 Pi Jokes.............................................................99 First Thousand Decimal Digits of Pi................101 First Thousand Hexadecimal Digits of Pi.........101 Physical Formulas with Pi................................102 About the Author............................................103 AUTHOR'S FOREWORD The number, pi (p), has fascinated mathematicians for thousands of years. At the time of Archimedes of Syracuse (287-212 BC), just three digits of pi were accurately known. Today, computers have calculated trillions of digits of pi. The purpose of this book is to inject some fun into this interesting mathematical constant. There are 100 mazes, one for each of the first hundred decimal digits of pi. Each maze page also contains an interesting pi fact. Properly constructed mazes are never impossible to solve, since there are simple rules by which a maze can be traveled by rote. The mazes in this book were generated by a computer program I wrote in the C programming language using an algorithm called recursive backtracking. Writing such a program is a common homework assignment in advanced computer science courses, but I needed to extend the code to add the decimal digits of pi and produce a publishable product. The mazes were produced as Scalable Vector Graphics (SVG) files. For the impatient, there's a companion book of solutions, The Amazing Number Pi (Solutions), Tikalon Press, ISBN: 978-0-9853325-9-4. This might be useful for a teacher who gives these mazes to his/her students as a fun assignment. Any teacher who purchases this book has my permission to make one copy on individual sheets, so each student can solve a few of the mazes as a fun assignment. v Digit-1 3.141592653 5897932384 6264338327 9502884197 1693993751 0582097494 4592307816 4062862089 9862803482 5342117067 Pi is also referred to as Archimedes' constant. In Germany, it's called die Ludolphsche Zahl (Ludolph's number) in honor of Ludolph van Ceulen (1540-1610), a German mathematician who calculating the first thirtyfive decimal digits of pi. 1 DEV GUALTIERI Digit-45 3.141592653 5897932384 6264338327 9502884197 1693993751 0582097494 4592307816 4062862089 9862803482 5342117067 One of Ramanujan's formulas for pi is as follows: 2 THE AMAZING NUMBER PI Digit-53 3.141592653 5897932384 6264338327 9502884197 1693993751 0582097494 4592307816 4062862089 9862803482 5342117067 In 1989, the brothers, Gregory V. Chudnovsky and David V. Chudnovsky, used an IBM 3090 computer to break the billion digit barrier in pi calculation. They calculated 1,011,196,691 decimal digits of pi using an infinite series discovered by Ramanujan. 3 DEV GUALTIERI Digit-69 3.141592653 5897932384 6264338327 9502884197 1693993751 0582097494 4592307816 4062862089 9862803482 5342117067 How many digits of pi are really needed? Physicists think that the smallest possible dimension of space is the Planck length, 1.6162 x 10-35 meters. To express the extent of the universe (about 1027 meters in diameter) to within a Planck length, only 62 digits of pi are needed. 4 THE AMAZING NUMBER PI Digit-98 3.141592653 5897932384 6264338327 9502884197 1693993751 0582097494 4592307816 4062862089 9862803482 5342117067 A formula for pi that's accurate to 52 decimal places: 5 DEV GUALTIERI The First Thousand Decimal Digits of Pi 3.141592653 0582097494 9821480865 8481117450 6442881097 1456485669 3724587006 6789259036 4330572703 8074462379 2983367336 8609437027 2000568127 2146844090 5420199561 0518707211 9502445945 1710100031 3598253490 8185778053 5897932384 4592307816 1328230664 2841027019 5665933446 2346034861 6063155881 0011330530 6575959195 9627495673 2440656643 7053921717 1452635608 1224953430 1212902196 3499999983 5346908302 3783875288 4287554687 2171226806 6264338327 4062862089 7093844609 3852110555 1284756482 0454326648 7488152092 5488204665 3092186117 5188575272 0860213949 6293176752 2778577134 1465495853 0864034418 7297804995 6425223082 6587533208 3115956286 6130019278 9502884197 9862803482 5505822317 9644622948 3378678316 2133936072 0962829254 2138414695 3819326117 4891227938 4639522473 3846748184 2757789609 7105079227 1598136297 1059731732 5334468503 3814206171 3882353787 7661119590 1693993751 5342117067 2535940812 9549303819 5271201909 6024914127 0917153643 1941511609 9310511854 1830119491 7190702179 6766940513 1736371787 9689258923 7477130996 8160963185 5261931188 7766914730 5937519577 9216420198 The First Thousand Hexadecimal Digits of Pi 3.243F6A888 82EFA98EC4 C29B7C97C5 BA698DFB5A 5F12C7F992 1574E69A45 54AEE7B54A 5F0CA41791 ED71577C1B 748986263E 486AF7C72E E169B87931 86B4BB9AFC DEC8032EF8 ACC50F6D6F 5E21C66842 960FA728AB F1651D39AF A5C33B8B5E 62363F7706 5A308D3131 E6C8945282 0DD3F84D5B C2FFD72DBD 4A19947B39 8FEA3F4933 41DC25A59B 8B8DB38EF8 D314B2778A 8144055CA3 993B3EE141 EAFD6BA336 4BFE81B662 45D5DE9857 F383F44239 F6E96C9A67 5133A36EEF 017666CA59 BEE06F75D8 1BFEDF7242 98A2E03707 1E638D0137 5B54709179 01ADFB7B8E 16CF70801F D7E0D95748 59C30D5392 E79DCB0603 F2FDA55605 96A2AAB10B 1636FBC2A2 C24CF5C7A3 8219361D80 5B1DC26230 2E0B4482A4 0C9C61ABD3 0B6C137A3B 3E82430E88 85C1207340 9B023D37D0 6 344A409382 7BE5466CF3 216D5D9897 1AFED6A267 2E2858EFC1 F728EB6587 AF26013C5D A180E6C9E0 C60E65525F 6B4CC5C341 BA9C55D741 2538128958 9CCFB21A99 2EB651B882 84200469C8 88F06A51A0 E4BA3BF050 8CEE861945 1A449F56C1 D724D00A12 2299F31D00 4E90C6CC0A 9FB1BD1310 E96BA7C904 6636920D87 18BCD58821 1B02328608 E8BB01E8A3 3AA55AB945 141E8CEA15 831F6CE5C3 6773B8F489 1487CAC605 893E81D396 F04A9E1F9B D2D8542F68 7EFB2A98A1 6F9FB47D84 6AA64ED3AA 48DB0FEAD3 THE AMAZING NUMBER PI Physical Formulas with Pi Period of a simple pendulum at small amplitude Force between two charged particles (Coulomb's law) The Heisenberg uncertainty relation for position and momentum Euler's equation for the buckling force for a slender column Stoke's law of fluid dynamics Cosmological constant Einstein's field equation of general relativity 7 DEV GUALTIERI About the Author Dev Gualtieri received his PhD in 1974 and had a thirty-five year research career in physics and materials science. He is listed as an inventor on thirty-five US patents, and on numerous international patents. His eclectic research interests included superconductivity, chemical thermodynamics, magnetism, electronics and computer science. At one time, he was an internationally recognized expert in crystal growth. Dr. Gualtieri is now retired, and he resides in Northern New Jersey with his wife, Anne. They have a son and daughter who reside with their spouses in Pennsylvania. 8
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