论勾股定理发现优先权标准

On the Discovery Priority Standard about Pythagorean Theorem

衡量勾股定理发现优先权有三个标准,一是特例表述、二是普遍化表述,三是证明。第一,中国这三者均首次出现在《周髀算经》,公元前十世纪的商高定理是特例;曲安京教授认为它体现"寓理于算"的证明思路;直到公元前七世纪陈子对话才有普遍化表述。第二,巴比伦泥版Plimton322的研究显示,六千年前巴比伦时代的毕达哥拉斯数组已经高达万位,未有证据表明巴比伦数表具有几何学含义,也未有证据说明巴比伦人掌握定理的一般表述。第三,很可能公元前六七世纪的毕达哥拉斯只是依据特例肯定所得结果,到了公元前四世纪的毕达哥拉斯学派晚期才实现证明;目前未见直接证据显示中国与巴比伦数学间交流,中国"形数统一"的证明传统区别于古希腊"算术与几何证明分离"传统,体现两种文化各自独特的数学传统。

There are three discovery priority standards in measuring Pythagorean Theorem,which are special case,generalization formulation and mathematical proof.In the first place,in China all these three formulations are firstly appeared in 'Zhou Bi Suan Jing',Shang Gao Theorem of 10th century BC is a special case,which is also thought of 'theorem proof in the count',until Chen Zi Theorem of 7th century BC has the generalization formulation.In the second place,studies of Babylon clay matrix Plimpton 322 indicate that Babylon's Pythagorean array reaches myriabit about six thousand years ago,there is no evidence that Babylon's Pythagorean array has geometry meaning and generalization formulation.In the third place,it is possible that Pythagoras perhaps get results by means of special case during 6-7th BC,until late Pythagorean School of 4th BC get proof of Pythagorean Theorem.There is no direct evidence of communication between China and Babylon mathematics,Chinese mathematics tradition of 'unity of shape and number' is different from ancient Greek tradition of 'separation of arithmetic from geometry'.