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圓周率

 割圓法：

劉徽


 以六觚之一面乘半徑，因而三之，得十二觚之冪(中國古代數學文獻中冪指幾何圖形的面積)。若又割之，次以十二觚之一面乘半徑，因而六之，則得二十四觚之冪。割之彌細，所失彌少。割之又割，則與園合體，而無所失矣。」《九章算術》第一卷 方田 劉徽注

 祖沖之

《隋书·律历志》中关于祖冲之圆周率的记载

 


科學精神：  

「親量圭尺，躬察儀漏，目盡毫釐，心窮籌策」。

堅持真理，反對“虛推古人"

 

「搜煉古今，博彩沈奧。

唐篇夏典，莫不揆量。

周正漢朔，咸加核驗。

罄策籌之思，究疏密之辯」。


祖沖之 駁議:

願聞顯據，以窮理實。

浮詞虛貶，竊非所懼。



中國求圓周率的限制：

圓周率以連分數( continued fraction)來表達 , 

但測量時是用丈呎寸分厘毫, 

又採用約率,密率

 

 

祖率

亞拉伯數學家 卡西 Jamshīd al-Kāshī

treatise of circumference

彭恩羚 slideplayer  

時間之問 (JD鏈)祖沖之 vs 戴法興 辯論:

zimedia  

幾何原本 與 九章算術. 

Van Ceulen,2 3 Ludolphine number

wikiwand


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