Soroban, Abacus


soroban 算盤 / 十呂盤 / そろばん Abacus, Abakus

This is the cover of a box for an abacus, Soroban.
The Kanji read : Hakodate Daruma Fuumi.
函館 だるま 風味
Maybe it is a special production for a food store of Hakodate in Hokkaido.


Checking a bit more about the abacus, I came about a great German/English page featuring all kinds of abacus (Abakus), some even made by a Daruma Company of Japan.

The following is quoted from this page of © J. Lütjens,
Mai 2004

Nr. 11
Neuer Soroban, gefertigt aus einem schwarz gefärbtenn Holzrahmen und mit 13 Reihen heller Holzperlen.Er gibt ein sehr schön kontrastreiches Bild. Das System 5+2 entspricht dem ursprünglichen chinesichen System und ist daher für einen japanischen Soroban eher ungewöhnlich. Aber es ist nun einmal so, denn dieser Soroban wurde hergestellt von der japanischen Fa. Daruma.
New soroban with 13 rows, system (5+2); all made of wood. Width: 305 mm; heigth: 125 mm.

Nr. 12

New colorful soroban with 13 rows, system (5+2); all made of wood. The back side is closed with a wooden plate.Width: 290 mm; heigth: 125 mm.

Nr. 17

Twin-soroban with sybolic meaning
This extraordinary item (two sorobans in one frame) is made of wood. It seems to be not suitable for calculating but mainly as a wall decoration. The meaning of the two opposite sorobans is probably "everything in life must be balanced". The translation of the four Chinese characters:

"good luck"
"long life"
"respect of daughters and sons"
"good luck"

Manufacturer: Daruma, Japan. Measures: width: 175 mm; height: 290 mm
Many thanks to my Korean colleague Prof. Dr. Kim Yuhn Su; he proposed the explanations above.

source : www.hh.schule.de



The Soroban - the traditional Japanese "natural calculating divice" - has unique advantages in the digital age. Soroban is the name given to the traditional Japanese abacus, or calculating frame, which is increasingly being seen as a valuable mathematical tool for a technological age. It is now certain that Soroban -teaching helps children to develop an active approach to learning, and greatly increased their powers of mental calculation. Development of logical thought processes and powers of concentration flow from the pleasurable disciplines involved in Soroban study.

Soroban is a world wide word and now you are able to look up this word in your webster dictionery.

When you study how to use soroban, you will receive lots of merits. Many educators and school teachers point out these merits of the soroban displaying the numbers the same way as in the decimal system as follows.

Easy to understand basic number systems such as base-ten and place values. Although the abacus is a concrete tool,the number as shown on the abacus is abstract, based upon the decimal system. This linkage with both the concrete and abstract help children to understand the concept of place value and base ten.

To understand concepts of carrying and borrowing in arithmatic.
Easy to understand the combinations of five and ten and the complement of numbers.
Children can determine themselves the calculation process step by step.
Easay to visualize the close relation between numbers and numerals.

Using a calculating Device motivates the children to have an active attitude toward study.The children really enjoy using Soroban, like to move the beads, they learn place value really effectively and they pick up the structure very fast. They learn and understand the number concepts better than just using paper and pencils.

Practicing soroban developes the children's ability of mental calculations.


The soroban is calculating instrument with a number of counting beads that slide back and for th along rods.

Each one-bead has the value of "one".
Each five-bead has the value of "five".

The columns toward the left always have higher values than those toward the right.

Always use the thumb and the forefinger to slide the beads back and forth.Hold other three fingers lightly.
Always use the thumb to add the one value beads.
Always use the forefinger to add the five value beads and to take away beads.


The Soroban in different Cultures

Abacus is probably the first of calculating devices. Encyclopædia Britannica traces the word abacus to the Phoenician abak (sand). American Heritage Dictionary points to the Greek word abax, which might have originated from Hebrew avak (dust). There is little doubt that Ancients used a flat surface with sand strewn evenly over it as a disposable tool for writing and counting. It's said that the great Archimedes was slain by a Roman soldier while concentrating on figures drawn in sand.

Later day abaci had grooves for small pebbles and later yet wires or rods on which counters could freely move back and forth. Each wire corresponded to a digit in a positional number system, commonly in base 10. A very curious state of affairs was mentioned by M. Gardner with a reference to K.Menninger. For more than 15 centuries the Greek and Romans and then Europeans in the Middle Ages and early Renaissance calculated on devices with authentic place-value system in which zero was represented by an empty line, wire or groove. Yet the written notations did not have a symbol for zero until it was borrowed by Arabs from Hindus and eventually introduced into Europe in 1202 by Leonardo Fibonacci of Piza in his Liber Abaci (The Book of Abacus). According to D. Knuth, counting with abaci was so convenient and easy that, at the time when only few knew how to write, it might have seemed preposterous to scribble some symbols on expensive papyrus when an excellent calculating device was readily available.

Chinese suan pan is different from the European abacus in that the board is split into two parts.

The lower part contains only five counters on each wire, the upper contains two. Digits from 0 through 4 are represented solely by counters in the lower part. The other five digits need an upper counter. E.g., 8 is represented by 3 lower counters and 1 upper counter.

I was reminded by Scott Brodie that Japanese soroban differs from its chinese relative in that it enforces carrying by containing only 4 counters "below the bar" and only 1 counter "above the bar" on each "wire". This eliminates dual representations of "fives" and "tens".
The Japanese call the low portion "earth" and the upper portion "heaven".

The applet represents an abacus close to the Russian variant where, for the ease of use, middle counters differ in color from all the rest. Given the advantage of home computers, the applet allows you to select a number system with bases from 2 through 16. Carrying of 1 to the next digit on the left is automatic. The entire interface with the applet is by clicking the mouse button. You can move a group of counters with a single click. Just point at the last counter you wish to move.
2005 Alexander Bogomolny


external link
The Abacus: The Art of Calculating with Beans.
Everything you wanted to know about Abacus.


Checking for Soroban and Daruma, I found this story.
Here is a pot for keeping tea powder, Chaire 茶入.

The form looks like the beads of a Soroban. It is supposed to look like a Daruma sitting in Zen meditation, so the pot is called "Daruma Tea Container".
- source - himeno/museum


. Legends and Tales from Japan 伝説 - Introduction .

Fukushima 福島県 - Nishi Aizu, 檜枝岐村 Hinoemata

rokusan yoke ロクサン除け "preventing Rokusan"
Rokusan yoke no majinai ろくさんよけのまじない
People who know a lot of spells (咒 / 呪 ju, majinai) do not go hunting very often.
Once a man had a stomach ache and asked an old man for a ritual to prevent Rokusan. He was healed quite fast.
Sometimes it helps to rub an abacus on the painful spot and say a spell, sometimes it helps to plaster an amulet with some pine resin (松脂 matsuyani) over the painful spot.

. Rokusan 六三 - Deity of Illness .

Kagawa 香川県 長尾町 Nagao

oomino 大箕 the great winnow
On the first birthday of a baby there is a special ritual. The baby is presented with a kind of rucksack containing (誕生餅) special birthday mochi and a winnow with a book, an abacus, a pen, scisors, a ruler, a hammer or other things with the wish for a bright future as a craftsman.

. mi み【箕】 winnow for grain .


soroban boozu 十呂盤坊主 "the Abacus Priest"
In some parts of Miyagi people hear the sound of a soroban being used in the shade unter a tree by the roadside.

He is also known as the ghost of a junior monk who committed suicide for his math mistakes.
He appears under a tree during the night and makes noise of using a soroban calculator.
- source : shotakotake.com -


wasan 和算(わさん)
the Japanese way of calculating

This is an original way of calculating, popular in Japan before the introduction of Western calculations.

Japanese mathematics
Kambei Mori 毛利勘兵衛 (Mori Kanbei) is the first Japanese mathematician noted in history
© More in the WIKIPEDIA !

One of its famous teachers (wasanka 和算家) was

CLICK for more photos

Seki Takakazu (Seki Kowa) 関孝和
寛永19年(1642年)3月? - 宝永5年10月24日(1708年12月5日))

He has been described as Japan's "Newton."
He created a new algebraic notation system, and also, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations.
Another of Seki's contributions was the rectification of the circle, i.e. the calculation of pi; he obtained a value for π that was correct to the 10th decimal place . . .
© More in the WIKIPEDIA !

He studied the calculation book 塵劫記 jinkooki (Jinkoki) by Yoshida Mitsuyoshi 吉田光由 (1598 - 1673), solved all the calculations given and added a few more of his own.

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Sangaku or San Gaku (算額; lit. mathematical tablet)
are Japanese geometrical puzzles in Euclidean geometry on wooden tablets which had dedicated to Shinto shrine during the Edo period (1603–1867) by members of all social classes.
Fujita Kagen (1765–1821),
Shimpeki Sampo (Mathematical problems Suspended from the Temple)
Sacred Mathematics: Japanese Temple Geometry
© More in the WIKIPEDIA !

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算木 wooden sticks for counting.


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In a Saijiki for Memorable Days,
the 8th of August is the Day of the Soroban.

8/08 歳時記:そろばんの日

kigo for early autumn


The sound of the balls clicking is heared as
pachi pachi パチパチ, a diversion of sound from hachi hachi,
the eighth day of the eighth month.

soroban ni hiji o motasete hirune kana

with my ellbow
on the abacus
I take a nap

Kobayashi Issa 小林一茶


the thumb doesn't move
if it ain't broke, don't fix it ..
on Soroban's day

Heike Gewi
Kigo Hotline, November 2010


- source : www.ebay.com


. Doing Business in Edo - 江戸の商売 .

soroban naoshi 算盤直し / そろばん直し
repairing abacus calculators

In the Edo period the soroban was widely used, even by the common people. Special teachers for children and later even for grown-ups in a kind of night-school made good business.

Repairmen walked along the streets and repaired the broken abacus そろばんなおし when the beads would not move any more or had come off. Sometimes the frame was broken and needed replacement.
The repairmen also carried a variety of new soroban in their backpack and sold them if needed.





sakuo said...

Truly this soroban page is great.
Your achievement is very valuable.
I can say in some future your Kigo work will come to the center of the highlight.

Anyway 素晴らしい知識です。


Gabi Greve said...

Thank you so much, Sakuo san!

Gabi Greve said...

Development of Wasan

This section introduces the various aspects that Wasan followed after Seki Takakazu (?-1708) based on two pillars: the master institution and the accomplishments of individual Wasan scholars.

Regarding the master institution, we exhibit introductory booklets for Wasan beginners, materials that show a competitive atmosphere in which Wasan scholars developed their mathematical attainment through friendly competition against each other, and a book that collected mathematical tablets used often by Wasan scholars as a means of announcing their results to the public. We also display a book that includes a diagram showing mentor-disciple relationships between Wasan scholars as a reference material.

This section of the exhibition also introduces materials related to some famous Wasan scholars in those days such as Nakane Genjun, Murai Chuzen, Arima Yoriyuki, and Aida Yasuaki.

In addition, we also exhibit materials to make audience aware of the aspect of Wasan as a hobby, which became conspicuous in the second half of the Edo period; essays about mathematics, and a book written by an author pretending to be a girl, and finally books that directly indicate examples of mathematical consummations attained by Wasan in the second half of the Edo period.

1 Hotei ryoshiki
2 Sanpo hyoron
3 Sureki soki
4 Shamei sanpu
5 Sugaku sosetsu

Wasan scholars
6 Kanja otogi zoshi Ten'nojiya Ichirobe, 1743.
7 Sanpo dojimon By Murai Chuzen
8 Shuki sanpo By Arima Yoriyuki.
9 Hoen kiko
10 Tetsujutsu by Aida Yasuaki

and more

Gabi Greve said...

Sangaku Proofs: A Japanese Mathematician at Work
J. Marshall UNGER

During many decades of national isolation, a mathematical tradition called wasan flourished in Japan independently of the advances of Enlightenment mathematics and virtually unknown to Europeans before the Meiji Restoration. Yet the brilliance of its practitioners, the wasanka, would surely have been admired by Leibniz or Euler had they been able to read their solutions to often difficult geometry problems. This interpretive translation of a suite of twenty-six related problems analyzed by Aida Yasuaki (1747–1817) gives readers unfamiliar with the premodern Japanese language access to a real wasan text. Instead of presenting and solving problems using modern techniques, Unger presents Aida’s own solutions, transcribing his calculations into familiar mathematical notation, highlighting connections between Aida’s work and both the mathematics of today and aspects of Japanese cultural history.
A specialist in the history of the Japanese language, he aims to bring fellow amateur mathematicians and interested professionals into contact with actual wasan methods, and to initiate a discussion of how wasan fits into the larger picture of premodern Japanese history.
J. Marshall UNGER
is professor of Japanese at Ohio State University. His research has focused on the history of Japanese, teaching Japanese as a second language, and writing systems of East Asia. Two of his books, The Fifth Generation Fallacy and Literacy and Script Reform in Occupation Japan, are available in Japanese.