The value of pi
AI-drafted · awaiting admin review
Aryabhata (499 CE) gave pi as 3.1416 and called it approximate. Archimedes, Ptolemy and Zu Chongzhi had good values earlier or at the same time. Madhava's 11-decimal value (c. 1400) was a world-leading result.
Earlier elsewhereMathematics & astronomy
Indian claim
Aryabhata was the first to calculate pi accurately, and he knew it was irrational.
Evidence for the Indian claim
- The Aryabhatiya (499 CE) gives the circumference of a circle of diameter 20,000 as 62,832, i.e. pi = 3.1416.
- Aryabhata calls this value asanna, 'approaching' or approximate; Nilakantha Somayaji (c. 1500) read this as saying pi cannot be expressed exactly.
- Madhava (c. 1400) used an infinite series to get pi correct to 11 decimal places.
Commonly credited to
Archimedes bounded pi between 223/71 and 22/7 in the 3rd century BCE, and Zu Chongzhi in China found 355/113 in the 5th century.
Evidence for the other claim
- Archimedes (c. 250 BCE) proved pi lies between 223/71 and 22/7.
- Ptolemy (2nd century CE) used 377/120, about 3.1417.
- Zu Chongzhi (5th century CE) gave 355/113, correct to six decimal places.
- Al-Kashi in Samarkand (1424) computed pi to 16 decimal places; Lambert proved pi irrational in 1761.
What historians and scientists say
Good approximations of pi were reached earlier in Greece and at about the same time in China. Aryabhata's value and his word 'approximate' are notable, and Madhava's series-based value was the best in the world in its time.