Editing Squaring the circle (section)

=== Construction by Kochański ===
{{multiple image
| image1 = Kochanski-1.svg
| caption1 = [[Adam Adamandy Kochański|Kochański's]] approximate construction
| image2 = Quadratur des kreises.svg 
| caption2 = Continuation with equal-area circle and square; <math>r</math> denotes the initial radius
| total_width = 600
}}
One of many early historical approximate compass-and-straightedge constructions is from a 1685 paper by Polish Jesuit [[Adam Adamandy Kochański]], producing an approximation diverging from <math>\pi</math> in the 5th decimal place. Although much more precise numerical approximations to <math>\pi</math> were already known, Kochański's construction has the advantage of being quite simple.{{r|kochanski1}} In the left diagram
<math display=block>|P_3 P_9|=|P_1 P_2|\sqrt{\frac{40}{3}-2\sqrt{3}}\approx 3.141\,5{\color{red}33\,338}\cdot|P_1 P_2|\approx \pi r.</math> 
In the same work, Kochański also derived a sequence of increasingly accurate rational approximations {{nowrap|for <math>\pi</math>.{{r|kochanski2}}}}
{{Clear}}