Compass-and-straightedge approximations, compared by cost and accuracy.
Exact construction is impossible: π is transcendental. The remaining problem is to approximate √π·r with the fewest lines and circles.
| c. 1650 BC | Rhind papyrus | π ≈ 3.1605 |
|---|---|---|
| 1685 | Kochański | 4.23 digits |
| 1882 | Lindemann | Exact construction proved impossible |
| 1913 | Ramanujan | 6.57 digits |
| 1914 | Ramanujan | 9.00 digits |
| 2022 | Beatrix | 13 strokes · 4.32 digits |
| 2026 | This search | 7 strokes · 8.05 digits |
One stroke is one line or circle; intersections are free.