| 对增乘开方及其相关问题的再探讨 |
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| 引用本文： | 段耀勇,郭书春.对增乘开方及其相关问题的再探讨[J].广西民族大学学报,2004,10(2):49-54. |
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| 作者姓名： | 段耀勇 郭书春 |
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| 作者单位： | 中国人民武装警察部队学院 河北廊坊 065000
(段耀勇),中国科学院自然科学史研究所 北京 100010(郭书春) |
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| 基金项目： | 国家自然科学基金资助项目(10171107) |
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| 摘 要： | 通过对开方术、带纵开方及增乘开方算法的比较分析,认为增乘开方的思想源于《九章算术》的开方术,带纵开方是中间的过渡阶段.增乘开方是将开方术归纳、推广的结果.而贾宪三角是记录了用增乘法得到的各乘方之廉.即:传统开方立成释锁释锁求廉本源(贾宪三角的造表法)增乘开方.因为贾宪三角中每一行的系数,都可由贾宪所创增乘方求廉草所得到的,因此贾宪不可能认识到贾宪三角中行与行之间系数关系.在开方算法的完善中体现出的中算的构造性特征及程序化的算法思想,至今仍有重要意义.
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| 关 键 词： | 贾宪 增乘开方 贾宪三角 |
| 文章编号： | 1007-0311(2004)02-0049-06 |
| 修稿时间： | 2003年12月18 |
The Zengcheng's Method of Extraction of a Root and JIA Xian's Arithmetical Triangle |
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| DUAN Yao-yong ,GUO Shu-chun.The Zengcheng's Method of Extraction of a Root and JIA Xian's Arithmetical Triangle[J].Journal of Guangxi University For Nationalities(Natural Science Edition),2004,10(2):49-54. |
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| Authors: | DUAN Yao-yong GUO Shu-chun |
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| Institution: | DUAN Yao-yong ~1,GUO Shu-chun~2 |
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| Abstract: | By contracting the method of extraction with "Daizong" method (MDZ, which is the general form of extraction and matches with solving numerical equations) and Zengcheng method (MZCH, which a kind of extraction method like Honer's method), it shows the extraction is MZCH's origin and MDZ's the bridge from extraction to MZCH. Moreover MZCH is the result of conclusion and deduction from the extraction. JIA Xian'S Triangle, the earliest in the world, records the coefficients of binomial, though JIA Xian didn't realized the relationship of quantity between two lines one after another. JIA Xian , in fact, created the MZCH in which the Zengcheng method is the soul. |
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| Keywords: | JIA Xian Zengcheng's Method JIA Xian's Triangle |
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