Pi is an irrational and transcendental number that is the ratio of a circle's circumference to its diameter. It has been calculated by mathematicians to billions of digits and occurs in formulas across many areas of science and mathematics. Throughout history, people have been fascinated by pi and have sought to calculate more of its digits, with modern computers now able to calculate it to over one trillion digits.

3. Copyright Audrey Weeks 2003
“People have calculated billions of digits of
pi because of the human desire to do
something that‟s never been done before .
When George Mallory was asked why he
wanted to climb Mt. Everest, he replied,
„Because it‟s there‟. Well, pi is certainly
here. Like the other planets, it‟s built into
the fabric of our physical universe and it will
always beFormal
Our Story of
explored.” Decimal Fractions Invented
Geometry Logarithms Invented
Pi Begins Begins Calculus Discovered
1650BC 600BC 300BC 1100 1600 2001
Thales Euclid Algebra Invented Computers &
Pythagoras Arabic Numerals (1,2,3...) Invented Calculators
(World's 1st Novel Written) Invented
(general public not even aware of the date)
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4. What is pi?
Copyright Audrey Weeks 2003
  diameter
circumference
The ratio of the circumference to the diameter of ANY circle
is constant. It is between 3 and 3 1 .It is close to but
7
NOT EQUAL to 3.14 or 22 .
7
Its digits will NEVER ...but will ALWAYS
terminate or continue to fascinate
repeat… mankind.
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5. Copyright Audrey Weeks 2003
Irrational &
Transcendental
• IRRATIONAL   22   3.14
7
Cannot be expressed as the quotient of 2 integers
This also means it cannot be written as a decimal for it
will never terminate or repeat.
• TRANSCENDENTAL Unlike 3 which solves x 2  3
No sequence of algebraic operations using
integers(powers,roots,sums,etc.)can be equal to its
value.
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6. Where Can we find pi?
Copyright Audrey Weeks 2003
IN EVERYTHING CIRCULAR (of course)
h
r
1
SA  2  dh   r 2
C  d h 1
V  3  r 2h
A   r2
r
SA   dh  2 r 2
V   r 2h
SA  4 r 2 SA  4 r 2 a
V  4  r3 V  2 2 r 2a
3
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7. Copyright Audrey Weeks 2003
occurs in hundreds of equations in many sciences including those
describing the DNA double helix, a rainbow, ripples
spreading from where a raindrop fell into water,
superstrings, general relativity, normal distribution,
distribution of primes, geometry problems, waves,
navigation....
Electricity - formulas for alternating currents and
radiation from radio & TV antennas
Clock designers use pi when designing pendulums for clock.
Medicine benefits from pi when studying the structure
the eye.
Aircraft designers use it to calculate areas of the skin of
the aircrafts.
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8. Copyright Audrey Weeks 2003
 (Leibniz) 

 41 
1
3

1
5

1
7

1
9

1

11 13
1

1
15

... 

 2  6  1  1  1  1  1  1  1  1 ... 

1 4 9 16 25 36 49 64 

 2 2 4
 2        
4 6 6 8 8 10 10 
 ... 
(John Wallis 1655) 1
 3 3 5 5 7 7 9 9 11 
 3
 2   
(Leonard Euler) 2
5
6
7 11 13 17 19

6 10 14 18 18
  
23
22

29 
30 
... 
3.1415926535897932384626433832795028841971693993751058209749445923078 ...

9. Copyright Audrey Weeks 2003
25  3.125 The Babylonians found the first known value for
8 Pi in around 2000BC -They used (25/8).
377  3.1416 Ptolemy (Alexandria, Egypt) 150 AD
120 Also used by Columbus on his voyage to the New World
223  3.1408450704... Archimedes (Syracuse, 287-212 BC)
71 22 Found pi to be between these two fractions.
 3.142857
7 This average error is only 0.0002!
355  3.141592920354 ... Tsu Ch’ung Chi
113 China, 450 AD
2143
4  3.14159265258... Srinivasa Ramanujan (India, 1887-1920)
22
4  97  2 1
1 If 16,539 replaced by ,  97  21 1  2143
22
2 1 2 1
1 4
3
1 1 (This is an irrational approximation.)
16539...
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10. Copyright Audrey Weeks 2003
Earliest Known Record of Pi
- 1650 BC
No number has captured the attention and
imaginations
of people throughout the ages as much as the
ratio of a circle’s circumference to its diameter.
The earliest known reference to Pi is
on a Middle Kingdom papyrus scroll,
written around 1650 BC by Ahmes the scribe.
He wrote this ratio as
“4 times the square of eight-ninths”
  8 2 
 4    256  approx. 3.1604938...
 9 81 
 less than 1% error ! 
 
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11. Archimedes, 250 Copyright Audrey Weeks 2003
3 10BC 3 7
71
 1
12.1 cm2

Area Circle =
Circumference of Circle Area Square = cm2
3.9

Diameter r
Area Circle
Area Square
but also ... r 6
5
4
3
2
1
He began with a regular hexagon 0
and kept doubling sides to a 96-gon! 3 4 5 6
Inner polygon perimeter / 2r
Later , the Chinese continued this doubling to ov er 3000 sides to ge t 3.14159.
Outer polygon perimeter / 2r
Archimedes derived the value of pi based on the area of a regular polygon inscribed within
the circle and the area of a regular polygon within which the circle was circumscribed. ...
3.1415926535897932384626433832795028841971693993751058209749445923078

12. I have proof!
Copyright Audrey Weeks 2003
1767 - Johann Lambert proved  irrational
First, he proved -
If x is rational, (x  0), then tan x cannot be rational.
1728-1777
i.e., If tan x is rational, then x must be irrational or 0. Swiss
 
 Since tan 4 = 1, 4 must be irrational. Q.E.D.
1794 - Adrien-Marie Legendre proved  2 irrational French
1840 - Joseph Liouville proved transcendental nos. exist
(used limits of continued fractions)
French
1873 - Charles Hermite proved e transcendental
 transcendental
French
1882 - Ferdinand Lindemann proved
German
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13. Copyright Audrey Weeks 2003
Starting at digit #772 - 9999998 occurs
largest 7-digit sum in the first million digits!
In 1st million, no “123456” but 012345 twice
123456789 first appears at 523,551,502nd digit
The fraction (22 / 7) is a well used number for Pi.
It is accurate to 0.04025%.
Another fraction used as an approximation to Pi
is (355 / 113) which is accurate to 0.00000849%
A more accurate fraction of Pi is(104348 / 33215).
This is accurate to 0.00000001056%.
There is no zero in the first 31 digits of Pi.
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14. Copyright Audrey Weeks 2003
1596 … Ludolph van Ceulen (Dutch) calculates 35 digits
(which were named the Ludolphine Number)
All by hand - months
1706 … John Machin calculates 100 digits
But Ferguson finds
1874 … William Shanks calculates 707 digits error in 527th onward
1947 … Ferguson (using desk calculator) finds 808 digits
1949 … ENIAC computer (DoD & U. of Pen.) finds 2037 digits
1973 … CDC 7600 (Paris) finds 1,000,000 digits (23 hrs)
1989 … 1,000,000,000 digits (USSR Chudnovsky brothers, NY)
2002… Hitachi SR8000(supercomputer)1.24 trillion digits (400hr.
It took a Hitachi SR 8000 supercomputer over 400 hours to compute pi to 1.24 trillion digits
Why still do this? …to find out more about pi
…to test computer architecture & efficiency
... to test software for accuracy and speed
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15. Copyright Audrey Weeks 2003
STAR TREK
The main computer of the Starship Enterprise is possessed by an
evil alien entity. Kirk, Spock and the gang have a plan to send the
entity into deep space but must first find a way to keep the computer
“busy” so it doesn’t detect their plan. Spock foils the evil computer
by commanding it to “compute to last digit the value of pi .”
The main characters are trying to uncover a secret hidden by a
mysterious puzzle. The legend is that the ancient Norse god, Thor,
created the puzzle so that when mankind developed enough to solve
the puzzle, we would be ready for the secret behind it!
Comedian John Evans once quipped: “What do you
get if you divide the circumference of a jack-o'-
lantern by its diameter? Pumpkin π .
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16. Copyright Audrey Weeks 2003
More misc. pi facts
Albert Einstein German
1879-1955
born 3 / 14 / 1879 (Pi-Day)
Symbol introduced by Leonard Euler, 1737
The first person to use the Greek letter Pi was
Welshman William Jones in 1706. He used it as an Swiss
abbreviation for the periphery of a circle with unit 1707-1783
diameter. Euler adopted the symbol and it quickly
became a standard notation.
Pi is it was taken from the Greek letter
"Piwas". It is also the 16th Greek alphabet.
Both π and the letter p are the
sixteenth letter in the Greek and
English alphabets, respectively
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17. Copyright Audrey Weeks 2003
Consider the following series of integers, each using one
more digit of pi: 3, 31, 314, 3141, 31415, 314159, 3141592,
etc. Out of the first 1000 numbers in this series, only 4 are
prime!
The world record for pi-recitation (from memory) is held by
Hiroyuki Gotu, age 21. 9 hours ... 42,000 digits!
Before the π symbol was used, mathematicians described pi
in round-about ways such as “quantitas, in quam cum
multipliectur diameter, proveniet circumferential,” which
means “the quantity which, when the diameter is multiplied
by it, yields the circumference.
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18. Copyright Audrey Weeks 2003
Since there are 360 degrees in a circle and pi is intimately connected
with the circle, some mathematicians were delighted to discover that
the number 360 is at the 359th digit position of
pi .
At position 763 there are six nines in a row. This is known as the
Pi is also referred to as the
Leonardo da Vinci (1452-1519) and artist
Albrecht Durer both briefly worked on
“squaring the circle,” or approximating pi .
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19. Copyright Audrey Weeks 2003
Pi was first rigorously calculated by one of the greatest
mathematicians of the ancient world, He
was so engrossed in his work that he did not notice that
Roman soldiers had taken the Greek city of Syracuse.
When a Roman soldier approached him, he yelled in
Greek The Roman soldier simply
cut off his head and went on his business.
Egyptologists and followers of mysticism have been fascinated for
centuries by the fact that the Great Pyramid at Giza seems to
approximate pi. The vertical height of the pyramid has the same
relationship to the perimeter of its base as the radius of a circle has
to its circumference
It is more correct to say that a circle has an infinite number of
corners than to view a circle as being cornerless .
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20. Copyright Audrey Weeks 2003
The Inspiration
The answer lay in the quest itself. From the exploration of new territories
to the conquest of space, men have always endeavored to push back the
frontiers of the known world and reveal the mysteries of the unknown.
Man’s essential character lies in his strength and determination in pushing
back his limits.
The Name
Resonant with history and mystery, is a link between past, present and
future. Pi is the universal number, the transcendental number, the ruling
number. Since Archimedes’ discovery of , more than 2000 years ago,
has been the object of a ceaseless quest. This letter of the Greek
alphabet is used in mathematics to express the constant ratio of the
circumference of a circle to its diameter. Today man is still seeking to
establish ’s unlimited decimals.
The Bottle
Designed by Serge Mansau for Givenchy, the bottle is a study in purity.
Its two sculpted backs, with their irregular density, modulate the amber
tones of the fragrance. The bottle’s broad, full base gives it a masculine
foundation and allure. To complete this construction, an innovative closing
system crowns 3.1415926535897932384626433832795028841971693993751058209749445923078 ...
the bottle. The curved shape of the cap, in bronze-colored

21. Copyright Audrey Weeks 2003
Oh, number Pi Pi Song
Oh, number Pi There are people who try
Your digits are unending, memorize the decimal
to
digits of pi. The people make
Oh, number Pi up songs and music based on
Oh, number Pi the digits of pi.
No pattern are you
sending.
You're three point one
four one five nine,
And even more if we had
time,
Oh, number Pi
Oh, number Pi
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22. Copyright Audrey Weeks 2003
A mnemonic is a verse
to assist memory
No . of letters=digit
May I have a large container of coffee? … (8)
How I want a drink, alcoholic of course, after the heavy lectures involving
quantum mechanics. All of thy geometry, Herr Planck, is fairly hard … (24)
Que j’aime à faire apprendre un nombre utile aux sages!
Immortel Archimède, artisite ingénieur, (31) Sir, I send a rhyme excelling
Qui de ton jugement peut priser la valeur? In sacred truth and rigid spelling.
Pour moi, ton problème eut de pareils avantages. Numerical sprites elucidate
For me the lexicon's dull weight. (21)
Dir, o Held, o alter Philosoph, du Riesengenie!
Sol y Luna y Mundo proclaman
Wie viele Tausendre bewundern Geister
al Eterno Autor del Cosmo. (11)
Himmlisch wie du und göttlich!
Noch reiner in Aeonen Wie? O! Dies  (24)
Wird das uns strahlen Mach ernstlich so vielen viele Müh’!
Wie im lichten Morgenrot! (30) Lernt immerhin, Jünglinge, leichte Verselein,
Wie so zum Beispiel dies dürfte zu merken sein!
Yes. I know a great geometric pi number which Mrs Weeks’ geometry
classroom studies carefully out at the Campbell Hall School. (21)
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23. Copyright Audrey Weeks 2003
CAN YOU FIND 402 digits of PI ?
“Circle Digits” For a time I stood pondering on
circle sizes. The large computer mainframe quietly processed
all of its assembly code. Inside my entire hope lay for figuring out an elusive expansion
value: pi. Decimals expected soon. I nervously entered a format procedure. The mainframe processed
the request. Error. I, again entering it, carefully retyped. This iteration gave zero error printouts in all - success.
Intently I waited. Soon, roused by thoughts within me, appeared narrative mnemonics relating digit to verbiage! The idea
appeared to exist but only in abbreviated fashion - little phrases typically. Pressing on I then resolved, deciding firmly about a
sum of decimals to use - likely around four hundred, presuming the computer code soon halted! Pondering these ideas, words
appealed to me. But a problem of zeros did exist. Pondering more, solution subsequently appeared. Zero suggests a punctuation
element. Very novel! My thoughts were culminated. No, periods, I concluded. All residual marks of punctuation - zeros. First digit
expansion answer then came before me. On examining some problems unhappily arose. That imbecillic bug! The printout I possessed
showed four nine as foremost decimals. Manifestly troubling. Totally every number looked wrong. Repairing the bug took much effort.
A pi mnemonic with letters truly seemed good. Counting of all the letters probably should suffice. Reaching for a record would be
be helpful. Consequently, I continued, expecting a good final answer from computer. First number slowly displayed on the flat
screen - 3. Good. Trailing digits apparently were right also. Now my memory scheme must probably be implementable. The
technique was chosen, elegant in scheme; by self reference a tale mnemonically helpful was assured. An able title suddenly
existed - “Circle Digits”. Taking pen I began. Words emanated uneasily. I desired more synonyms. Speedily I found
my (alongside me) Thesaurus. Rogets is probably an essential in doing this, instantly I decided. I wrote and
erased more. The Rogets clearly assisted immensely. My story proceeded (how lovely!) faultlessly.
The end, above all, would soon joyfully overtake. So, this memory helper story I
incontestably complete. Soon I will locate publisher. There a narrative will 360 words - ignore periods
I trust immediately appear, producing fame. other punctuation = 0
words > 9 letters = 2 digits
THE END. word for no. = digit
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24. Copyright Audrey Weeks 2003
“Fools Rush In”
Author of Bill - Edwin J. Goodman, M.D. of Indiana - Introduced Jan. 18, 1897
Preamble: “A bill for an act introducing a new mathematical truth and offered as a contribution to
education to be used only by the State of Indiana, free of cost by paying any royalties
Body: whatever on the same, provided it is accepted and adopted.”
“...It has been found that the circular area is to the quadrant of the circumference, as the
area of an equilateral rectangle is to the square on one side. The diameter employed as the
linear unit according to the present rule in computing the circle’s area is entirely wrong…”
(This makes no sense … if meant to be “eq. tri”, then   16  9 here!)
3
…“Furthermore, it has revealed the ratio of the chord and arc of 90o as 7:8, and the ratio of
the diagonal and one side of a square as 10:7, and the ratio of the diameter and
circumference is 5/4:4 (so now   3.23, 2  2.041)
“In further proof of the value of the author’s proposed contribution to education … and
State of Indiana” … (claims the Dr. solved other classic unsolvable problems). [sq. circle]
(These ancient problems have been proven to be unsolvable.) [trisect angle]
Feb. 5 - House votes 67 to 0 in favor; bill forwarded to the Senate
Feb. 10 - Pf. Waldo (Purdue, checking school grant) overhears; coaches Senate
Feb. 12 - Senate votes to postpone further consideration of this bill
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25. Copyright Audrey Weeks 2003
Pi Day is a holiday held to celebrate
the mathematical constant π (pi). Pi
Day is observed on March 14 (3/14 in
American date format), due to π being
equal to roughly 3.14. Sometimes it is
celebrated on March 14 at 1:59 p.m.
(commonly known as Pi Minute). If π is
truncated to seven decimal places,
it becomes 3.1415926, making
March 14 at 1:59:26 p.m.
At 9:26:53 on Pi Day 2015, the
date will be 3/14/15 at 9:26:53,
corresponding to 3.141592653.
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26. Copyright Audrey Weeks 2003
Larry
Shaw, the
creator of
The first Pi Day celebration
Pi Day, at
was held at the San Francisco
Exploratorium in 1988, withthe Larry Shaw,
staff and public marching
around one of its circular Exploratori of
the creator
Pi Day, at the
spaces, and then consuming um Exploratorium
fruit pies; the museum has PI day is
since added pizza pies to Celebrated
its
Pi Day menu
by pie
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27. Copyright Audrey Weeks 2003
Provides an Lead to
intellectual developments in
challenge. computer
Because it technology.
exists. Pi is the most
Lead to recognized
important mathematical
discoveries in constant in the
modern world. Scholars
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28. Copyright Audrey Weeks 2003
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