Chinese abacus subtraciton8/7/2023 In total, learning the basics of the abacus required memorizing about 150 rules that had to be recited or sung while applied. Once the students learned to add and subtract with these types of rules, they began to memorize the multiplication and division tables also in the form of verses or rymas. In the event that we cannot proceed with such rules because we do not have the necessary beads at our disposal, then, we use the non-trivial rules listed in the table. "to add two, activate two lower beads" or "to subtract 6, deactivate both an upper and a lower bead". Nine cancel ten, return five, cancel fourĬlearly, the table above does not contain the trivial rules eg. Nine raise four, cancel five, forward ten Seven cancel ten, return five, cancel twoĮight raise three, cancel five, forward tenĮight cancel ten, return five, cancel three Seven raise two, cancel five, forward ten borrow one from the left column), return nine Here are rules/rhymes/verses that appear on it and whose interpretation is left to the reader: We have an example in English of what these types of rules were like thanks to the booklet: The Fundamental Operations in Bead Arithmetic, How to Use the Chinese Abacus by Kwa Tak Ming, Printed in Hong Kong (unknown publisher and date), a work aimed to English-speaking Filipinos according to the author. It may be of interest to know that in the past people learned the abacus without having prior knowledge of mathematics, in particular without knowing anything like an addition or subtraction table instead they memorized a series of mnemonic rules, verses or rhymes, short phrases in Chinese that indicated which beads had to be moved to result in the addition or subtraction of one digit to/from another digit. If it is mentioned here, it is because regardless of its limited usefulness it is a very interesting exercise that can be difficult at first, resulting in a small challenge that can lead the reader to interesting reflections on the order of movement of the fingers in particular, on whether carries and borrows should be done before or after.Ĭhapter Extending the 123456789 exercise proposes its daily use as a way to perfect our understanding of beading. Therefore, the alternation of direction of operation should be considered a secondary matter. In the 19th century, the well-known Canadian-American astronomer Simon Newcomb, a renowned human computer, recommended the practice of adding and subtracting from left to right using pencil and paper in the introduction to his tables of logarithms. If the reader has already studied the modern abacus he knows for sure why it is preferable to operate from left to right, and this is not only a question of the use of the abacus. Some old books on the abacus, for instance, Mathematical Track ( Shùxué Tōngguǐ 數學通軌) by Kē Shàngqiān (柯尚遷) (1578), demonstrate the addition using an alternating direction of operation with the obvious intention of saving hand movements. We dedicate the following chapter: Use of the 5th lower bead to this subject. Its use is demonstrated in some ancient books such as: Computational Methods with the Beads in a Tray ( Pánzhū Suànfǎ 盤珠算法) by Xú Xīnlǔ 徐心魯 (1573), but over time it ceased to appear in the manuals, perhaps as a non-fundamental technique it was no longer explained in the concise books of the past but surely it continued to be taught verbally, as a trick to abbreviate the operations. The lower fifth bead can be used in addition and subtraction operations just like its companions. Of which the first is by far the most important.ĥth lower bead First two pages of the Pánzhū Suànfǎ 盤珠算法 (1573) alternating rightward and leftward operation to save hand displacements.use of the lower fifth bead to simplify the operations.The only two additional points to consider are: There is hardly any difference between addition and subtraction with a modern abacus or a traditional one, if the reader already knows how to perform these two operations fluently with a modern abacus, he will also do well with a traditional one. Everything else has to be decomposed into a sequence of addition and subtraction. Addition and subtraction are the only two possible operations on any type of abacus. With any abacus type, addition is simulated by gathering the sets of counters representing the two addends, while subtraction is simulated by removing from the set of counters representing the minuend a set of counters representing the subtrahend.
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