```The Amazing
Number Pi
Dev Gualtieri
http://www.tikalonpress.com
ISBN: 978-0-9853325-8-7
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
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
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
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
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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