engleski

The "Law of Large Integers" in Historical Mathematical Textbooks

After the Indoarabic decimal positional system was introduced in Europe, through- out many centuries textbooks on elementary arithmetic, intended for beginners, had a more or less fixed organisation of content, in most cases starting with chapters on numeration. These chapters, as a rule, contained one or more examples of large integers the purpose of which was simply to be named (read out loud), sometimes also vice versa. This tradition apparently began with the two first texts that significantly contributed to the spread of the decimal system in Eu- rope, the Latin translations of al-Khwarizmi’s treatise on decimal arithmetic, and Leonardo’s Liber Abaci, containing examples of reading a 16- digit and a 15-digit number respectively. Throughout the centuries, the order of magnitude of these introductory numbers increased, in general up to some 30 digits, but in some cases to over 60 digits. In this paper we examine the development and extent of this characteristic of introductory arithmetic textbooks from the period 13th–19th century, and the conditions which lead to this, now extinct, practice, as well as its purpose in mathematical education in the mentioned periods.

history of mathematics education, large integers, teaching basic arithmetic

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