Aryabhata Writes the Aryabhatiya and Approximates Pi
A 23-year-old Indian astronomer defines the sine function and gets pi to four decimal places
Quick facts
- Aryabhata's dates
- 476 CE to 550 CE
- Aryabhatiya completed
- 499 CE, age 23
- Pi value given
- 3.1416
- Trigonometric contribution
- Sine table at 90 degrees/24 intervals; versine
What happened
Aryabhata, born in 476 CE probably near modern Patna, finished the Aryabhatiya in 499 CE at the age of 23, a treatise of 118 verses summarizing Indian mathematics and astronomy up to that point. In it he gave a rule for the circumference of a circle that reduces to pi equal to 3.1416, a value scholars consider the most accurate approximation among the ancients and very close to the modern figure. Aryabhata also gave a table of sine values at intervals of 90 degrees divided by 24, introduced the versine into trigonometry, and, according to later scholarly assessment, extremely likely knew both the symbol for zero and the numerals of the place-value system that his work depended on for its calculations.
Why it matters
The Aryabhatiya shows India developing sophisticated trigonometry and a highly accurate value of pi centuries before either reached Europe, and Aryabhata's decimal place-value methods, along with the zero concept his work implies, fed directly into the number system al-Khwarizmi would later carry into the Islamic world and, eventually, into Europe by way of Fibonacci.
How we know
The Aryabhatiya survives as a complete Sanskrit text and was extensively commented on by later Indian mathematicians across the following millennium, giving historians a continuous chain of transmission and interpretation back to the original 499 CE composition.
Sources
- The Schools' Observatory, Liverpool John Moores University. Aryabhata · General sourceschoolsobservatory.org · Cited as a "reference" source (no stronger domain match). · Link is live and its text matches the event's key terms (Jul 2026)
- MacTutor History of Mathematics, University of St Andrews. Aryabhata I · Reputable sourcemathshistory.st-andrews.ac.uk · The domain "mathshistory.st-andrews.ac.uk" is on our Reputable source registry. · Link is live and its text matches the event's key terms (Jul 2026)
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