古代印度数系的历史发展

Development of the Theory of Ancient Indian Number System

通过研读和比对原典文献,文章对印度数系及与其相关的记数法、数词、数字的发展演变进行追根溯源。确认在印度文明初期已有十进制记数法。数学的发展对数系的扩张和数字的发明起最直接的作用:从早期的单位分数到后来用除法来定义分数;"零"的出现不晚于6世纪,但零和负数的运算律的完善却和7世纪代数学研究密切相关;无理数(卡拉尼数)在公元前6世纪由几何产生,随着计算的深入其也从原来单纯的几何概念抽象为一般意义上的二次根式。印度数字刚诞生时可能仅是数词的简化符号,5世纪左右引入了十进位值制,在8世纪前演变成了包含符号0在内的完整体系。印度的算板笔算传统在其发展过程中起了关键性的作用。

The development of the Indian number system together with the numeration and numerals was examined in this paper by studying and comparing the original texts.It is confirmed that the decimal system has been in existence in the earliest period of the Indian civilization.The evolvement of mathematics directly forms the development of the number system and the invention of numerals：the fractional quantity is defined by the division instead of the early unit fractions;the complete rules of zero appears before the 6 th century and negative numbers are related to the Indian algebra in the 7 th century;the irrational numbers（）emerge together with the geometry and＂ ＂is generally understood as quadratic radical through the development of computation.At the beginning,Indian numerals came from the simplified marks of the word-numerals.In about the5 th century,the decimal system was adopted.Before the 8 th century,a complete system including0 was formed.It is believed that in this progress the Indian calculating board and manual computation has played a pivotal role.