Adam Adamandy Kochański的π近似值：算法重建
Adam Adamandy Kochański's approximations of π: reconstruction of the algorithm
AI总结：
本研究重建了Adam Adamandy Kochański1685年论文中未完整公布的π有理近似值生成算法，指出其已接近发现连分数与π的收敛分数。
摘要：
Adam Adamandy Kochański在1685年发表于《Acta Eruditorum》的论文《Observationes cyclometricae》中，提出了一种用于圆求长的近似尺规作图法。鲜为人知的是，该论文第一部分包含了一组有趣的π有理近似序列。Kochański仅对生成这些近似值的算法给出了部分解释，同时承诺后续会公布细节，但始终未能兑现。我们重建了完整的算法并讨论了其部分性质，还提出Kochański当时已非常接近发现连分数与π的收敛分数。
英文摘要：
In his 1685 paper "Observationes cyclometricae" published in Acta Eruditorum, Adam Adamandy Kochański presented an approximate ruler-and-compass construction for rectification of the circle. It is not generally known that the first part of this paper included an interesting sequence of rational approximations of π. Kochański gave only a partial explanation of the algorithm used to produce these approximations, while promising to publish details at a later time, which has never happened. We reconstruct the complete algorithm and discuss some of its properties. We also argue that Kochański was very close to discovery of continued fractions and convergents of π.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
