07-22-2026, 09:44 PM
Approximations of pi
Summary
The history of approximating π reflects one of mathematics’ longest and most fascinating pursuits, spanning more than four thousand years. Early civilizations, including the Babylonians and Egyptians, produced simple numerical estimates, while the Greek mathematician Archimedes introduced a rigorous geometric method using inscribed and circumscribed polygons, establishing the foundation for future calculations. Over the centuries, mathematicians in China, India, the Islamic world, and Europe steadily improved the accuracy of π, with notable contributions from Zu Chongzhi, Madhava, Jamshīd al-Kāshī, and Ludolph van Ceulen.
Practical approximations such as 22/7 and the remarkably accurate 355/113 became widely used because they are easy to remember and compute. Modern mathematics developed powerful tools including infinite series, continued fractions, products, and rapidly converging algorithms like the Bailey–Borwein–Plouffe and Chudnovsky formulas. Today, computers calculate trillions of digits of π, not because such precision is needed for everyday applications, but to advance computational mathematics, test algorithms, and push the limits of high-performance computing.
ARTICLE
Summary
The history of approximating π reflects one of mathematics’ longest and most fascinating pursuits, spanning more than four thousand years. Early civilizations, including the Babylonians and Egyptians, produced simple numerical estimates, while the Greek mathematician Archimedes introduced a rigorous geometric method using inscribed and circumscribed polygons, establishing the foundation for future calculations. Over the centuries, mathematicians in China, India, the Islamic world, and Europe steadily improved the accuracy of π, with notable contributions from Zu Chongzhi, Madhava, Jamshīd al-Kāshī, and Ludolph van Ceulen.
Practical approximations such as 22/7 and the remarkably accurate 355/113 became widely used because they are easy to remember and compute. Modern mathematics developed powerful tools including infinite series, continued fractions, products, and rapidly converging algorithms like the Bailey–Borwein–Plouffe and Chudnovsky formulas. Today, computers calculate trillions of digits of π, not because such precision is needed for everyday applications, but to advance computational mathematics, test algorithms, and push the limits of high-performance computing.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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