The document discusses the history and properties of pi (π). It describes how various ancient civilizations like the Babylonians, Hebrews, and Egyptians approximated pi. The Greeks studied pi's relationship to circles, cones, and cylinders. Over centuries, mathematicians like Machin, Euler, and Lambert improved approximations of pi and proved its irrationality. With modern computers, pi has been calculated to extreme accuracy. The document also notes how pi is

2. Team Members…
Grace Henry
Haima Ronald
Lekshmi Dev.S
Preetha G. Lopez
Rahul Lekshman
Suriya S. Kumar
Shameer Mehboob

3. What is pi??
A number can be placed into several categories based on its
properties. Is it prime or composite? Is it imaginary or real? Is it
transcendental or algebraic? These questions help define a
number's behaviour in different situations. In order to understand
where π fits in to the world of mathematics, one must understand
several of its properties: π is irrational and π is transcendental.
Another important concept to understand is that of how π is
calculated and how the methods have changed over time.
π is:-
"1: the 16th letter of the Greek
alphabet...
2 a: the symbol pi denoting the ratio of
the circumference of a circle to its
diameter b: the ratio itself: a
transcendental number having a value to
eight decimal places of 3.14159265"

4. The computation of Pi to 10,000
places may be of no direct
scientific usefulness. However, its
usefulness in training personnel to
use computers and to test such
machines appears to be
extremely important. Thus the
mysterious and wonderful Pi is
reduced to a gargle that helps
computing machines clear their
throats.

5. The early Babylonians and
Hebrews used “3”as a value
for Pi.
Later, Ahmed, an Egyptian
found the area of a circle .
Down through the ages,
countless people have
puzzled over this same
question, “What is Pi?
The Greeks found Pi to be
related to cones, ellipses,
cylinders and other geometric
figures.

6. LEIBNITZ (1671) Pi= 4(1/1-1/3+1/5-1/7+1/9-
1/11+1/13+...)
WALLIS Pi= 2(2/1*2/3*4/3*4/5*6/5*6/7*...)
MACHIN (1706) Pi=16(1/5- 1/(3+5^3) +1/(5+5^5) -
1/(7+5^7)+...) x
- 4(1/239 -1/(3*239^3) + 1/(5*239^5)-
...)
SHARP (1717) Pi= 2*Sq.Rt(3)(1-1/3*3 + 1/5*3^2 -
1/7*3^5...)
EULER (1736) Pi= Sq.Rt(6(1+1/1^2+1/2^2+ 1/3^2...))
BOUNCKER Pi= 4 --- 1+1 --- 2+9 --- 2+25 +...

7. Approximations of Pi
Philosopher Date Approximation
Ptolemy around 150 A.D. 3.1416
Zu Chongzhi 430-501 AD. 355/113
al-Khwarizmi around 800 A.D. 3.1416
al-Kashi around 1430 A.D. 3.14159265358979
Viète 1540–1603 3.141592654
Roomen 1561–1615 3.14159265358979323
Van Ceulen around 1600 A.D. 3.1415926535897932384
6264338327950288

8. Pi in everyday life
 We use it for
Drawing, machining, plans, planes, buildings, bridges, g
eometry
problems, radio, TV, radar, telephones, estimation, testin
g, simulation, global paths, global positioning, space
science, orbit calculation, Space
ships, satellites, Speedometers at vehicles… etc.
 Pi is used by every career whether you are a electrical
engineer, statistician, biochemist, or physicist. Pi is
indeed a necessity for life.

9. Pi facts
 ”Pi Day” is celebrated on March 14. The official
celebration begins at 1:59 p.m. to make an appropriate
3.14159 when combined with the date.
 Albert Einstein was born on Pi Day (14/3/1879) in Ulm
Wurttemberg, Germany.
 Pi goes on for ever
 Decimals have no pattern and don’t repeat.

11. The development of high speed
electronic computing equipment
provided a means for rapid
computation. Inquiries regarding the
number of Pi’s digits
-- not what the numbers were
individually, but how they behave
statistically -- provided the motive for
additional research.

12. • The early Babylonians and Hebrews used three as a value for
Pi. Later, Ahmes, an Egyptian found the area of a circle .
Down through the ages, countless people have puzzled over
this same question, “What is Pi?"
• From 287 - 212B.C. there lived Archimedes, who inscribed in
a circle and circumscribed about a circle, regular polygons.
• The Greeks found Pi to be related to cones, ellipses, cylinders
and other geometric figures.

13. Anyone for Pi?

14. Pi Day is an unofficial holiday
commemorating the mathematical
constant π (pi). Pi Day is observed on
March 14 (or 3/14 in month/day date
format), since 3, 1 and 4 are the three
most significant digits of π in the
decimal form. In 2009, the United
States House of Representatives
supported the designation of Pi Day.
Pi Approximation Day is
observed on July 22 (or 22/7 in
day/month date format), since the
fraction 22⁄7 is a common
approximation of π.

15. .
Pi Pie at Delft University

16. 22/7 exceeds π
 Proofs of the famous mathematical result that the rational
number 22/7 is greater than π (pi) date back to antiquity.
 22/7 is a widely used Diophantine approximation of π(the
approximation of real numbers by rational numbers).
 It is a convergent in the simple continued fraction expansion
of π. It is greater than π, as can be readily seen in the
decimal expansions of these values:
 The approximation has been known since antiquity.
Archimedes wrote the first known proof that 22/7 is an
overestimate in the 3rd century BCE, although he may not
have been the first to use that approximation. His proof
proceeds by showing that 22/7 is greater than the ratio of
the perimeter of a circumscribed regular polygon with 96
sides to the diameter of the circle. Another rational
approximation of π that is far more accurate is 355/113.

18. The first record of an individual
mathematician taking on the problem of
π (often called "squaring the circle," and
involving the search for a way to cleanly
relate either the area or the
circumference of a circle to that of a
square) occurred in ancient Greece in
the 400's B.C. (this attempt was made
by Anaxagoras)
In the late Greek period (300's-200's
B.C.), after Alexander the Great had
spread Greek culture from the western
borders of India to the Nile Valley of
Egypt, Alexandria, Egypt became the
intellectual centre of the world. Among
the many scholars who worked at the
University there, by far the most
influential to the history of π was Euclid.
While π activity stagnated in Europe,
the situation in other parts of the world
was quite different. The Mayan
civilization, situated on the Yucatan
Peninsula in Central America, was quite
advanced for its time. The Mayans were
top-notch astronomers, developing a
very accurate calendar. In order to do
this, it would have been necessary for
them to have a fairly good value for π.
The Chinese in the 5th century
calculated π to an accuracy not
surpassed by Europe until the 1500's.
The Chinese, as well as the
Hindus, arrived at π in roughly the same
method as the Europeans until well into
the Renaissance, when Europe finally
began to pull ahead.

19. Leonardo Da Vinci and Nicolas
Copernicus made minimal
contributions to the π endeavour,
but François Viète actually made
significant improvements to
Archimedes' methods.
The efforts of Snellius,
Gregory, and John
Machin eventually
culminated in algebraic
formulas for π that
allowed rapid calculation,
leading to ever more
accurate values of π
during this period.
In the 1700's the
invention of calculus by Sir
Isaac Newton and Leibniz
rapidly accelerated the
calculation and
theorization of π.
Using advanced
mathematics,
Leonhard Euler
found a formula for
π that is the fastest
to date.
In the late 1700's
Lambert (Swiss) and
Legendre (French)
independently
proved that π is
irrational.
Although Legendre
predicted that π is also
transcendental in 1882.
Also in the 18th
century, George Louis
Leclerc, Comte de
Buffon, discovered an
experimental method for
calculating π.
Pierre Simon
Laplace, one of the
founders of
probability
theory, followed up
on this in the next
century.
Starting in 1949 with the ENIAC
computer, digital systems have
been calculating π to incredible
accuracy throughout the second
half of the twentieth century.

20. The End!