History of Number Pi

Klasické a španělské gymnázium, Brno

Dividing time slots

1. Egypt, Mesopotamia, China 2. Ancient Greek 3. Middle age 4. Renaissance 5. 18. Century 6. 19. Century 6. 20. Century 7. Movies 8. Present

what is actuallyπ?

Number Pi is an irrational number so it can't be expressed by a mathematical fraction. In basic problems we can use the fraction 22/7 or more exact 335/13.A different name for Pi is Ludolf‘s number – named by a Dutch mathematician Ludolafa von Ceulena.He was the first who calculated π for 35 decimal places.

E G Y P T

We can find some mathematical discoveries even in the Egyptian civilization.They used to write with hieroglyphics onto roll paper (papyrus). The most important discovery was Rhind's (Ahmos's) papyrus, which was discovered in Thebes in the middle of the 19. Century. It includes a collection of 87 mathematical problems. Because of that we know that Egyptians handled algebra and geometry perfectly.

E G Y P T

Rhind's papyrus includes even the first calculations of area of a circle and because of

That, Egyptian thought that the value of π is 3,1605. Egyptians were also thinking

that circle can be inscribed in a square.

E G Y P T

M E S O P O T A M I A

One of the oldest Babylonian charts relating to geometry of circles is called YBC7302. There‘s a diagram of a perfect circle and three figures. Above the diagram there‘s number 3 (perimeter), 9 () and inside of the circle there‘

M E S O P O T A M I A

Thanks to the simple Babylonian calculations it becomes obvious that Babylonians thought that the value of Pi was 3.

C H I N A

Already around the year 200 AD, the major Chinese work, entitled "Mathematics in nine books„ was created, filling a comparable role, same as the European Euclid‘s collection („Elements„).

C H I N A

Thanks to an educated chieftain named Wang Fan, the value of Pi was already known to be approximately 3.15555. Later on, Chinese knowledge expanded with Liu Hui, who gave us a more exact value, that is 3.14159.

A N C I E N T G R E E C E

Ve starověkém Řecku hrál největší roli Archimédes. Ten vypočítal číslo pí pomoci vepsaných a opsaných mnohoúhelníků. Původně měly mnohoúhelníky 12 stran, později 24, 48 a 96… Dostal tak pro pí horní a dolní hranici.

The major mathematician in ancient Greece was Archimedes who calculated the number thanks to inscribed and circumscribed polygons. Originally, the polygons had 12 sides, then 24, 48, 96… And Archimedes got to the upper and lower limits.

A N C I E N T G R E E C E

Archimedes‘ most important works include: The Method, On Spirals, Measurement of a Circle, Quadrature of the Parabola, Conoids and Spheroids, On Spheres and Cylinders,…

Archimedova metoda výpočtu π

M I D D L E A G E S

Middle Ages were characterized by the "dark interim" between Graeco-Roman medieval and modern period. The beginning of the Middle Ages, is generally considered to be the fall of Rome in 476 AD and the end date is considered to be the year 1492ndThe term Middle Ages was first used by the Renaissance thinkers in the late fifteenth century.

M I D D L E A G E S

The Middle Ages was a period of significant cultural decline.All of the scientific theories were declined by the church and said to be the devil‘s work.Because of the church a lot of eminent mathematicians were burned alive, including Giordano Bruno, Galileo Galilei, …

M I D D L E A G E S

It is no wonder that mathematics registered only a small progress during these ages. Until the Renaissance, Europe's math knowledge was roughly the same as the Babylonians‘ 2000 years ago.The history of number Pi wasn‘t an exception as there wasn‘t accomplished any major improvement in this area. That was until the year 1593 when Viete discovered the infinite product of nested radicals.

Leonardo z Pisy- FIBONACCI (around 1170 - 1250)can be seen as the most notable mathematician of the Middle Ages. His work wasn‘t outdone until the Middle Ages – Modern ages turn.

M I D D L E A G E S

M I D D L E A G E S

Leonardo‘s book Practica geometriae is also partly dedicated to geometric problems. This file is divided into 3 section. The third part mainly deals with the „measurement of figures“ (e.g. triangle, square, rectangle, polygon and circle). There‘s also a general guidance on how to calculate the perimeter and the area of a circle plus a specific formula for a circle that is 14 in diameter. Pi is used in the form of 22/7.

T H E B E G I N N I N G O F T H E R E N A I S S A N C E

It was the most progressive coup the humanity experienced so far. Renaissance is saturated with discoveries leading to the refinement of mathematical methods.During this time period the number π was mainly associated with the need of accurate numerical values of constants.In addition to the Indo-Arabic numerals and decimal fractions there were another two means of numerical calculations, namely trigonometric functions and logarithms.

T H E B E G I N N I N G O F T H E R E N A I S S A N C E

Francois Viète (1540 - 1603) significantly contributed to the development of modern algebra by adding lots of new terminological words, some of which, such as ‚negative‘ or ‚coefficient‘ persisted to modern age. Applying Archimedes' method he calculated π (using a regular 392,216-square) accurately up to nine decimal places. Later on he expressed π as an infinite product. The process was that he put the area of a polygon with n sides to the area of a polygon with 2n sides.

T H E B E G I N N I N G O F T H E R E N A I S S A N C E

Ludolf van Ceulen (1540 - 1610)In 1596, he published his article Van den Circkel with the accurate value of π up to 20 decimal places. The paper ends with: "Whoever wants to, can go even further." And his work (‚De Aritmetische en Geometrische fondamenten‘)accurately indicates the value of π even up to 35 digits. His never ending hunt for numbers made an impression on the Germans thus they began to call π „The Ludolf‘s number".

T H E B E G I N N I N G O F T H E R E N A I S S A N C E

James Gregory (1638 - 1675)

One of the very important discoveries were the arctg series.Gregory realized that the area under the curve 1 / (1 + x ^ 2) in the interval (0, x) is the arctan x.

Isaac Newton (1642 - 1727)

He found the converging series for π. He determined a method of how to calculate the derivative variables and vice versa and how to find the integral of the function.

1 8 . C E N T U R Y

In 1706 Machin found this mathematical relation:And the symbol of π set

Thanks to this ralation, π was refined to 707 decimal places.

In 1761 Lambert describes π as an irracional number

1 9 . C E N T U R Y

Joseph Liouville (1809-1882)- French professor of Mathematics- In 1840 he was the first one to prove the

existence of the transcendental numbers

Transcendental number: a real or complex number that is not algebraic

1 9 . C E N T U R Y

Ferdinand von Lindemann (1852-1939)- German mathematician- In 1882, he demonstrated that Pi is a

transcendental number- his approach was similar to the methods used

nine years earlier by Charles Hermite- he has also proved that e (the base of natural

logarithms) is transcendental.

2 0 . C E N T U R Y

The technical revolution has helped π to unroll even further. Eventually, people started to realize that they don‘t need to limit themselves by using only pen and paper to work with numbers and so the world began operating computers.

2 0 . C E N T U R Y

The last person to calculate Pi on paper and with no technical help is Ferguson. In 1946 he publishes this number calculated up to 620 decimal places.And additionally in 1947 (this time using a desktop calculator) he correctly forecasts Pi to 808 digits.

2 0 . C E N T U R Y

In 1949 a computer was used for calculating for the first time (Eniac) and π is determined to 2000 decimal places.

2 0 . C E N T U R Y

Rapid technological innovation and new computer models now enable even faster and more accurate calculations of π.

http://upload.wikimedia.org/wikipedia/commons/4/4e/Eniac.jpg

2 0 . C E N T U R Y

Computer model The number of decimal places designated by / for what time / in what year

ENIAC 2 037/70 hours/1949

NORC 3 089/13 minutes/1955

Pegasus 10 021/33 hours/1957

IBN „704“ 10 000/40 minutes/1958

IBN „7090“ 20 000/39 minutes/1961

CDC „6600“ 500 000/28 hours 10 minutes/1967

Film Pi(1998, USA)

“Max is a genius mathematician, who is able to combine his unique mind with the newest technology. With the help of one of his inventions, he's trying to find out how will the shares increase..His real goals go even further and these activities begin early interest representatives of the Orthodox Jewish sects and senior people from Wall Street ... "

Film Pipas (2013, Spain )Short film about 2 girls who don't know what is number Pi, one of the girl's boyfriend o and the non- existing Pilar.

For watch here

Today

Today there isn't any mathematical fild which doesn't use this number. We use number Pi in geometry, algebra and mathematics analysis. And as a consequence number Pi becomes more important. With the arrival of modern technology it became obvious that number Pi isn't just in mathematical world. Computers are dependant on π.

Today

People often ask themselves that why number π has so many digits . In the past like in 17. and 18. Century the mathematicians were fighting and competing amongst each other. Today we use number Pi if we want to test computers. A computer passes this test if its result is the same (several thousand digits) as in other computers.

And for conclusion some playthings

Number of letters in the word gives us the value of number Pi. 1. But I must a while endeavour to reckon right (9 digits)2. How I want a drink, alcoholic of course, after the heavy lectures involving quantum

mechanics (15 digits)

Sources

● JUŠKEVIČ, P. Adolf. Dějiny matematiky ve středov ku. Praha: Academia, 1977

● CRILLY, Tony. Matematika. 50 myšlenek, které musíte znát. Bratislava:Slovart, 2010.

● Bakalářská práce- Bc. Eliška Ponikelská (str.44, 45, 46)● Internetový portál Pi 314. Francois Viete:

http://www.pi314.net/eng/viete.php● http://www.studovna4u.cz/matematika/ludolfovo-cislo-pi%CF%80● http://www.csfd.cz/film/35661-pi