Pi Through the Years

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Earliest Written Form of Pi: Egypt

1650 B.C.

Egypt: The Rhind Papyrus formulated for the area of a circle that makes pi equal to (16/9)2 ≈ 3.1605.

Earliest Written form of Pi: Babylon

1600 B.C.

Babylon: Clay tablet that has inscribed a geometrical statement stating that pi is equal to 25/8 = 3.1250.

Shulba Sutras

600 B.C.

Found in India, the text enriched in mathematical equations just like a textbook, makes pi equal (9785/5568)2 ≈ 3.088.

Hebrew Bible

400 B.C.

Describe the construction of The Temple of Solomon, saying that the ceremonial pool's dimensions include a diameter of 10 cubits and circumference of 30 cubits. This would leave to assumption that pi would equal around 3, if the pool is circular.

Archimedes

250 B.C.

First recorded algorithm for calculating pi's value by using the help of polygons. Essentially, he computed upper and lower bounds of pi, by drawing a hexagon inside and outside of a circle. Then doubled the number until reaching a 96-sided polygon. By doing this, he proved that pi equaled 223/71 < π < 22/7 and/or (3.1408 < π < 3.1429).

Ptolemy

150 B.C.

Gave pi the value of 3.1416, which he obtained from Archimedes polygonal algorithms.

Rabbi Nehemiah

150 A.D.

Explained his version of pi to be valued around 3 and 1 seventh.

Liu Hui

265 A.D.

Created a polygon based algorithm and used to calculate a 3,072 sided polygon to figure out the value of pi 3.1416.
Later invented a faster way of calculating pi and the rounded value of 3.14 by using a 96 sided polygon. Knowing that the differences in area of the two polygons, he figured out the polygons made a geometric factor with the number 4.

Zu Chongzhi

480 A.D.

Calculated pi equaled around 355/133 by using Hui's algorithm, applying it to a 12,288 sided polygon. With a correct assumption of the first 7 digits of pi in the form of "3.141592920" remained the most accurate approximation of pi for the next 800 plus/minus years to come.

Aryabhata

499 A.D.

Indian astronomer, used the value of pi in 3.1416 form in his "Aryabhatiya"

Fibonacci

1220 A.D.

Computed 3.1418 by using polygonal method, separate from Archimedes' method.

Jamshid Al-Kashi

1424 A.D.

Persian astronomer produced 16 digits using a polygon with 3×2 (to the 28th power) sides, which stood as the world record for the next 180 years.

First written description of Infinite Series

1500 A.D.

Used by Indian Astronomer Nilakantha Somayaji in his "Tantrasamgraha".

First concept of Proofs

1530 A.D.

Yuktibhasa was one of the firsts to show the written use of proofs.

Francois Viete

1579 A.D.

French mathematician achieved 9 digits with a polygon of 3x2 (to the seventeenth power) sides.

First Infinite Sequence

1593 A.D.

First discovered in Europe. This is the form of an infinite product, rather than a sum, which in present day used in more pi calculations. Founded by French mathematician Francois Viete.

Adriaan von Roomen

1593 A.D.

Flemish mathematician valued pi around 15 places.

Ludolph van Ceulen

1596 A.D.

Dutch mathematician reached 20 digits in the value of pi. Later on went to break his record further 35 digits. (Now having the nickname Ludolphian Number)

Willebrord Snellius

1621 A.D.

Dutch scientist who reached pi valued pi back down to 34 places.

Christoph Grienberger

1630 A.D.

Brought pi back up to 38 digits, which at this time, remained the most accurate approximation achieved without a computer using the polygonal algorithms.

John Wallis

1655 A.D.

Second founded of Infinite Sequence. (Also with the use of product.)

John Machin

1706

Used the Gregory-Leibniz series to form an algorithm that was much faster. With the new formula, pi over 4 equals four arctan one fifth minus arctan one over two hundred thirty-nine, his version of pi reached to 100 places. Used as the most accurate method for calculating, well even into the computer era.

Johann Heinrich Lambert

1761

Proved that pi was irrational.

Adrien-Marie Legendre

1794

French mathematician proved that pi squared is also irrational.

Zacharias Dase

1844

Used the Machin-like formula to calculate 200 decimals of pi in his head.

Ferdinand von Lindemann

1882

German mathematician that proved pi is transcendental, or not a non-constant polynomial.

Computer Era: John Wrench and Levi Smith

1949

American mathematicians reached the value of pi to 1,120 places with using a desk calculator.

George Reitwiesner and John von Neumann

1951

Leaders of a mathematical team, was able to prove pi's value to 2,037 places with a calculation that took about 70 hours of computer time on the ENIAC computer.

The Study of Pi..

1960

The study and re-calculation of Pi continues on well into the early 2000s. Constantly changing and expanding. Challenging the boundaries of the mathematical world.