Turning a circle into a straight line
sourceinterpretation
Published in Acta Eruditorum in 1685. With compass and straightedge it produces a segment almost exactly equal to half the circumference of the circle.
Step 1 of 5 — a circle of radius r with diameter AB.
- Construction BD
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- True πr
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- Error
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On a clock dial the error falls below what a seventeenth-century workshop could machine. At the radius of the Earth it grows to nearly four hundred metres.
The claim that this is an approximation designed for making rather than for calculating is our interpretation — Kochański nowhere argues it in those terms.
Text description of the instrument
The construction yields a segment of length r·√(40/3 − 2√3) ≈ 3.141533·r, short of πr by about six millionths of the radius. At a radius of 150 mm the error is 8.9 µm; at the radius of the Earth it grows to nearly 380 metres.