Squaring the circle

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Compass-and-straightedge approximations, compared by cost and accuracy.

Strokes and correct digits of π

Exact construction is impossible: π is transcendental. The remaining problem is to approximate √π·r with the fewest lines and circles.

c. 1650 BCRhind papyrusπ ≈ 3.1605
1685Kochański4.23 digits
1882LindemannExact construction proved impossible
1913Ramanujan6.57 digits
1914Ramanujan9.00 digits
2022Beatrix13 strokes · 4.32 digits
2026This search7 strokes · 8.05 digits

One stroke is one line or circle; intersections are free.