The History of PI

Mathematics Project

Team Members…

Grace Henry

Haima Ronald

Lekshmi Dev.S

Preetha G. Lopez

Rahul Lekshman

Suriya S. Kumar

Shameer Mehboob

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"

As said in the beginning, “There is more to Pi than meets the eye

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.

Pi histo

ryThe 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.

Some people became famous by discovering ways to calculate Pi

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 +...

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. 3.14159265358979323846264338327950288

Pi in everyday life

We use it for Drawing, machining, plans, planes, buildings, bridges, geometry problems, radio, TV, radar, telephones, estimation, testing, 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.

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.

THIS ANIMATION DEMONSTRATES THE IDEA OF PI

Digit dancing

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.

Where can you find mathematical PI?

• 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.

It’s curious how certain

topics in mathematics show

up over and over. In the late

1940's two new mathematical

streams (electronic computing

and statistics) put Pi on the

table again.

Anyone for Pi?

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.

Pi DAY

Date abstractions from π

Pi Day is observed on March 14 because of the date's representation as 3/14 in month/day date format. This representation adheres to the commonly used approximation of 3.14 for π.

The fractional approximation of π,22⁄7, resembles the date July 22 in the day/month format, where it is written 22/7. Pi Approximation Day is therefore observed on July 22.

Pi Pie at Delft University

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.

When mathematicians are faced with quantities which are hard to compute, they try, at least, to pin them between two other quantities which they can compute. The Greeks were not able to find any fraction for Pi. Today we know that Pi is NOT a rational number and cannot be expressed as a fraction.

Pi is everywhere

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.

The History of Pi

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.

The search for PI

The End!