4,000 years of π
From Archimedes to al-Kāshī, 1,700 years of work moved the record from 2 decimal places to 16. In the 76 years from ENIAC to 2025 it went from 2,037 to 300 trillion.
Each point is a record: the number of correct decimal places of π known at that date, and who found them. The vertical axis is logarithmic, so every gridline is ten times the one below. Hover or tap a point for the story.
The time axis is stretched toward the present: antiquity is squeezed into the left edge so the last four centuries get room. Hollow dashed point: a claimed record that was wrong.
Race your browser
This runs Machin's 1706 formula, π/4 = 4 arctan(1/5) − arctan(1/239), in exact integer arithmetic inside this page. It is the same formula Machin, Shanks and ENIAC used. The digits appear as they become certain, and your browser gets a point on the chart.
The records
Correct decimal places, not digits claimed. Where someone published more digits than were right, the note says so.
In the atlas
The polygon era rests on the method of exhaustion and Archimedes' bounds. The series era starts with Mādhava's series and becomes general with power series. The machine era needs the stored-program computer, and every record since the 1980s multiplies its huge numbers with the fast Fourier transform.
None of this ever finishes: π is irrational, and Lindemann's 1882 proof that it is transcendental also settled that no ruler-and-compass construction squares the circle.