History Of π

Mathematics Project

ARCHIMEDES

HISTORY OF A Π The early Babylonians and Hebrews used “3”as a value

for π.

Later, Ahmed, an Egyptian found the area of a circle .

Down through the ages, countless people have

puzzled over this same question, “What is π?

The Greeks found Pie to be related to cones, ellipses, cylinders and other geometric figures.

Π 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.

π is used by every career whether you are a electrical

engineer, statistician, biochemist, or physicist. π is indeed a necessity for life.

PIE DAY

”Pie 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 Pie Day (14/3/1879)

in Ulm Wurttemberg, Germany.

π goes on for ever Decimals have no pattern and don’t repeat.

DIGITAL DANCING

The development of high speed electronic computing equipment provided a means for rapid computation. Inquiries regarding the number of π digits

-- not what the numbers were individually, but how they behave statistically -- provided the motive for additional research.

CALCULATING PIE

Pie is known to be an irrational number it means that the digits never end or repeat in any known way.

In 1949, a computer calculated 2,000 digits and the race was on.

Millions of digits have been calculated, with the record held (as of September 1999) by a supercomputer at the University of Tokyo that calculated 206,158,430,000 digits.

FIRST 100 DIGITS OF Π

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

Π IS EVERYWHERE

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 computer. The Greeks were not able to find any fraction for Pie. Today we know that π is NOT a rational number and cannot be expressed as a fraction.

FORMATION OF Π

π is a name given to the ratio of the circumference of a circle to

the diameter. π was founded by Archimedes in 1761.

Π IS THEORETICAL

It appears to have been Archimedes who was the first to obtain a theoretical calculation of π. He concluded the following: 223/71<pi<22/7

Archimedes used inequalities very sophisticatedly here to show that he knew π did not equal 22/7. He never claimed to have found the exact value.

It has become one of the most prominent missions of the scientific community to calculate π more and more precisely

THE NOTATION OF Π The first to use the symbol π with its current

meaning was William Jones in 1706. He was a Welsh mathematician.

Euler adopted the symbol in 1737 and it soon became a standard.

William Jones Leonhard Euler

SOME PEOPLE BECAME FAMOUS BY DISCOVERING WAYS TO CALCULATE Π

Some people were “dedicated” enough to actually spend incredible amounts of time and effort continuing the calculation of π.1699: Sharp gets 71 correct digits1701: Machin gets 100 digits1719: de Lagny gets 112 correct digits 1789: Vega gets 126 places 1794: Vega gets 136 places1841: Rutherford gets 152 digits1853: Rutherford gets 440 digits1873: Shanks calculates 707 places of which 527

were correct

Thank - you

Presentation by:

Devanshi Garara and

Vaibhav Mehra.