中国古算术语“金蝉脱壳”的含义及其演变

The Meaning and Evolution of Chinese Ancient Calculation Term “jinchan tuoqiao”

“金蝉脱壳”是用加减解决乘除运算的一种算法,是中国古代数学中,特别是珠算中比较重要、浅显易懂的乘除计算方法,后来发展成较为复杂的“凑倍乘除”“剥皮”“扒皮”等算法。一些珠算辞书或著作对“金蝉脱壳”等术语进行了解释,但各有不同,同时也存在一些缺点。文章通过追溯其源流并分析不同算书中“金蝉脱壳”及其相关术语的含义,对“金蝉脱壳”的数学含义及演变过程进行了新的研究。

“Jinchan tuoqiao”(金蝉脱壳) is a calculation method that solves the multiplication and division operations by addition and subtraction. It is an important and easy-to-understand multiplication and division calculation method in ancient Chinese mathematics, especially in abacus. Later it developed into a more complicated calculation method such as “coubei chengchu”(凑倍乘除),“baopi”(剥皮),“bapi”(扒皮). Some abacus dictionaries or books have explained “jinchan tuoqiao” and its related terms, but each of them is different, and there are also some shortcomings. By tracing the origin of the term “jinchan tuoqiao” and analyzing the meaning of this term and its related terms in different mathematical books, the paper studies the mathematical meaning and evolution process of “jinchan tuoqiao”.