Thread by @JoeAgneya

#PiApproximationDay
Here is the Indian story of Pi-

Yajnavalkya 2000BCE->339/108=3.1388..(.09% error)
Baudhayana 1700BC 3.08
Jainas 400BC 3.16
Aryabhata 499CE 3.1416
Govindaswami 800CE 3.14159265
Madhava,1370 3.14159265358
Nilakanta 1480, 'Folks!Pi is irrational'

Ramanuja 1914:

Yajnavalkya is the first named mathematician in history associated with pi. No name from contemporary Egypt or Mesopotamia is known. Of the many values in Shatapatha Brahmana, 339/108 is the best. The history of Science & Math should begin with his name.
Courtesy: Kosla Vepa

While Aryabhata used the practically elegant value of 3.1416, he was also aware that pi can only be 'approached' and is in fact an irrational number. This makes him the first mathematician to realize this.

Madhava derived the infinite series expansion of Pi with which he obtained the value correct to 11 decimal places. His successors, perhaps Jyeshtadeva (1550 CE) attained accuracy to 17 decimals, all massive world records then.

These formulas reached Europe through Jesuits.

Ramanujan's formula and its variants are today used by supercomputer algorithms for calculating pi correct to millions of decimals of accuracy! What a true genius he was to discover such powerful equations all by himself with no training!

History of Pi in other civilizations-

Egypt 2500-2000 BCE
3.16045

Mesopotamia 2000 BCE
3.125 =3+1/8

Ancient China 1200BCE
3

Bible 500BCE
3

Ptolemy 150CE
3.1416

Han Shu 130CE
3.1622=sqrt(10)

Liu Hui 263CE
3.14159

Tsu Chung 480CE
3.1415926

Al-Khwarizmi 800CE
3.1416