The AmazingNumber Pi

Dev Gualtieri

http://www.tikalonpress.com

Copyright © 2013 D.M. Gualtieri

All rights reserved.

ISBN: 978-0-9853325-8-7

CONTENTS

Table of ContentsAuthor's Foreword...............................................vPi Digits 1-24......................................................1History................................................................1Pi as a Number...................................................7Calculating Pi....................................................22Pi Digits 25-49..................................................25Pi Digits 50-74..................................................50Feats of Strength..............................................59Calculating with Pi............................................63Miscellaneous Facts..........................................70Pi Digits 75-100................................................75Mnemonics.......................................................93Pi Approximations.............................................97Pi Jokes.............................................................99First Thousand Decimal Digits of Pi................101First Thousand Hexadecimal Digits of Pi.........101Physical Formulas with Pi................................102About 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.

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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 thirty-five decimal digits of pi.

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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:

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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.

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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.

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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:

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The First Thousand Decimal Digits of Pi

3.141592653 5897932384 6264338327 9502884197 1693993751 0582097494 4592307816 4062862089 9862803482 5342117067 9821480865 1328230664 7093844609 5505822317 2535940812 8481117450 2841027019 3852110555 9644622948 9549303819 6442881097 5665933446 1284756482 3378678316 5271201909 1456485669 2346034861 0454326648 2133936072 6024914127 3724587006 6063155881 7488152092 0962829254 0917153643 6789259036 0011330530 5488204665 2138414695 1941511609 4330572703 6575959195 3092186117 3819326117 9310511854 8074462379 9627495673 5188575272 4891227938 1830119491 2983367336 2440656643 0860213949 4639522473 7190702179 8609437027 7053921717 6293176752 3846748184 6766940513 2000568127 1452635608 2778577134 2757789609 1736371787 2146844090 1224953430 1465495853 7105079227 9689258923 5420199561 1212902196 0864034418 1598136297 7477130996 0518707211 3499999983 7297804995 1059731732 8160963185 9502445945 5346908302 6425223082 5334468503 5261931188 1710100031 3783875288 6587533208 3814206171 7766914730 3598253490 4287554687 3115956286 3882353787 5937519577 8185778053 2171226806 6130019278 7661119590 9216420198

The First Thousand Hexadecimal Digits of Pi

3.243F6A888 5A308D3131 98A2E03707 344A409382 2299F31D00 82EFA98EC4 E6C8945282 1E638D0137 7BE5466CF3 4E90C6CC0A C29B7C97C5 0DD3F84D5B 5B54709179 216D5D9897 9FB1BD1310 BA698DFB5A C2FFD72DBD 01ADFB7B8E 1AFED6A267 E96BA7C904 5F12C7F992 4A19947B39 16CF70801F 2E2858EFC1 6636920D87 1574E69A45 8FEA3F4933 D7E0D95748 F728EB6587 18BCD58821 54AEE7B54A 41DC25A59B 59C30D5392 AF26013C5D 1B02328608 5F0CA41791 8B8DB38EF8 E79DCB0603 A180E6C9E0 E8BB01E8A3 ED71577C1B D314B2778A F2FDA55605 C60E65525F 3AA55AB945 748986263E 8144055CA3 96A2AAB10B 6B4CC5C341 141E8CEA15 486AF7C72E 993B3EE141 1636FBC2A2 BA9C55D741 831F6CE5C3 E169B87931 EAFD6BA336 C24CF5C7A3 2538128958 6773B8F489 86B4BB9AFC 4BFE81B662 8219361D80 9CCFB21A99 1487CAC605 DEC8032EF8 45D5DE9857 5B1DC26230 2EB651B882 893E81D396 ACC50F6D6F F383F44239 2E0B4482A4 84200469C8 F04A9E1F9B 5E21C66842 F6E96C9A67 0C9C61ABD3 88F06A51A0 D2D8542F68 960FA728AB 5133A36EEF 0B6C137A3B E4BA3BF050 7EFB2A98A1 F1651D39AF 017666CA59 3E82430E88 8CEE861945 6F9FB47D84 A5C33B8B5E BEE06F75D8 85C1207340 1A449F56C1 6AA64ED3AA 62363F7706 1BFEDF7242 9B023D37D0 D724D00A12 48DB0FEAD3

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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

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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.

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