For the abacus, soroban, suanpan... from ancient books
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| Image from Yoshida's Jinkoki (塵劫記) (Edo period) |
Traditional division
Traditional division, kijohou, guī chúfǎ (帰除法), used since at least the 13th century with counting rods until the 20th century, is today the most precious lost arcane of beads arithmetic to recover.
The 5th lower bead
How to use it to simplify calculations a bit. Extracted from the oldest book dedicated exclusively to the abacus: Xú Xīnlǔ's Pánzhū Suànfǎ (盤珠算法) (1573).HTML, PDF
Read also: The Five Bead Advantage - demonstrating how a 5th earth bead has its advantages. By Hannu Hinkka and Totton Heffelfinger.
Roots a la Knott
This writing is a personal elaboration on the methods of obtaining roots described in Cargill G. Knott's 1885 article: The Abacus, in its Historic and Scientific Aspects.
Square root: the traditional way
Prof. Kato's method, Hankukuhou, Bàn jiǔjiǔ fǎ (半九九法) using traditional division and traditional division arrangement.
Using a fourth finger on the suanpan
This is simply a curiosity but one day I realized that I was using four fingers while working a square root ...HTML, PDF
Clearing the nine trays (In project)
Traditional addition and subtraction practice without exercise sheets. How to extend it.
Finger mouvement order
Carries & borrows, first or last?HTML, PDF
Where to place divisor / multiplier (In project)
On the left or on the right?
Traditional multiplication (In project)
The abacistic inverse of traditional division in traditional arrangement. It is in project, in the meanwhile you can read:
In Totton Heffelfinger's website (archive.org)
Division by powers of two
Fractions with a denominator that is a power of two can be written exactly as a decimal with a finite number of digitsHTML, PDF
Counting rods
籌,筹 chóu in Chinese; 算木 sangi in Japanese.The most versatile and powerful abacus ever... and the slowest. The origin of all the techniques used in every fixed bead abacus.This is a long-term project for me.
If you don't have a traditional abacus jet...
You use Soroban Trainer ,forked from Masaaki Murakami. In 2:5 mode use Shift+Click to set/unset the suspended bead( or use the on-screen [ShiftLock] button).or...
Download this java application by David Bagley that can be configured as 3:5 and you can use the third upper bead instead of the suspended bead. It is multi-platform but requires that you have a JVM (Java Virtual Machine) installed.
