Traditional abacus techniques

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.

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)

Prof. Kato's method, Hankukuhou, Bàn jiǔjiǔ fǎ (半九九法) using traditional division

Cargill Gilston Knott, a Scottish physicist and mathematician considered the father of modern seismology, wrote his own vision on the Chinese / Japanese abacus in 1885. This writing is a personal elaboration on the methods of obtaining roots described in his article: The Abacus, in its Historic and Scientific Aspects.

One day I realized that I was using four fingers while working a square root ...

Traditional addition and subtraction practice without exercise sheets. How to extend it.

In project

Under certain ancient techniques it seems to underlie a principle of least action tending to minimize movements, time and effort in calculations with abacus.

In project

Carries & borrows, first or last?

On the left or on the right?

In project

The abacistic inverse of traditional division in traditional arrangement

In project, in the meanwhile you can read:

• Traditional multiplication (archive.org)

• Modern multiplication (archive.org)

In Totton Heffelfinger's website (archive.org)

Fractions with a denominator that is a power of two can be written exactly as a decimal with a finite number of digits

In project

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.

Go to the Soroban Trainer page

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.