Egypt: The Rhind Papyrus formulated for the area of a circle that makes pi equal to (16/9)2 ≈ 3.1605.
Babylon: Clay tablet that has inscribed a geometrical statement stating that pi is equal to 25/8 = 3.1250.
Found in India, the text enriched in mathematical equations just like a textbook, makes pi equal (9785/5568)2 ≈ 3.088.
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.
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).
Gave pi the value of 3.1416, which he obtained from Archimedes polygonal algorithms.
Explained his version of pi to be valued around 3 and 1 seventh.
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.
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.
Indian astronomer, used the value of pi in 3.1416 form in his "Aryabhatiya"
Computed 3.1418 by using polygonal method, separate from Archimedes' method.
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.
Used by Indian Astronomer Nilakantha Somayaji in his "Tantrasamgraha".
Yuktibhasa was one of the firsts to show the written use of proofs.
French mathematician achieved 9 digits with a polygon of 3x2 (to the seventeenth power) sides.
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.
Flemish mathematician valued pi around 15 places.
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)
Dutch scientist who reached pi valued pi back down to 34 places.
Brought pi back up to 38 digits, which at this time, remained the most accurate approximation achieved without a computer using the polygonal algorithms.
Second founded of Infinite Sequence. (Also with the use of product.)
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.
Proved that pi was irrational.
French mathematician proved that pi squared is also irrational.
Used the Machin-like formula to calculate 200 decimals of pi in his head.
German mathematician that proved pi is transcendental, or not a non-constant polynomial.
American mathematicians reached the value of pi to 1,120 places with using a desk calculator.
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 and re-calculation of Pi continues on well into the early 2000s. Constantly changing and expanding. Challenging the boundaries of the mathematical world.