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Welcome to the

This site is a part of the 

Sourcee: The fundamental operations in bead arithmethic, how to use the Chinese abacus. 
Published in Hongkong without year.


Domains of the collection
History and function of abacus

Basic remarcs:
In this abacus-online-museum you can see items from different Asian and European countries. Even though of  the diversity of the collection, all abacuses can be reduced to two basic types: the Asian and the Russian abacus. But the collection doesn't follow this structure.

1. Roman abacus
For a big size foto please click on the idex.
The Roman abacus can be seen as the first pocket calculator. 
This item shown here is a bronze made replica. It is re-designed after 
a drawing from the 17th century. (Source: Ifrah, page 112.)


1st. the Asian type (in three variants)

Criteria: round beads, positioned in a system of (2+5) beads on each rod. This is the traditional design of a Chinese abacus with an upper section and a lower section of beads. Even today it is relatively common.  Criteria: The beads are double cone shaped. They are positioned in a system of (1+5) beads on each rod. This simplified construction was developed in Japan toward the close of the nineteenth century. Criteria: The beads are also double cone shaped. They are positioned in a system of only (1+4) beads on each rod. This most simplified construction was developed in Japan around 1920.



2nd. the 
Russian type

A simple system of
10 beads on each rod
without any function of "more-unit-beads".

When abacuses from different countries are displayed, it doesn't mean that those are representative county-specific types or variants. The only reason that the collection is coutrywise structured is given through the origin of the items. Differences are to see in number of rods, measures, materials and sometimes scurrilous constructions.

Enter the collection here:

Abacuses from the 
following countries:


Special constructions:  abacuses for blind people
abacus related calculation and counting devices 
for the beginners in elementary math


abacuses for several purposes:
(advertising, decoration, rubbish etc.)


Links to web-sites about history and function of abacus, schools and institutions:
Luis Fernandes Very detailed sites with scientific explanations and lots of examples
Benjamin Wrightson Recommendable and good understandable introduction, calculating examples, international references (currently in German),
Sergei Frolov Short information about Russian abacuses
Jörn Lütjens "THE  ABACUS – ONE  OF  THE  OLDEST  CALCULATION  DEVICES - Some information on historical facts, systems, special constructions and calculation examples". Revised edition of an article which is published in the proceedings of the 9 th International Meeting of Slide Rule Collectors 19-20 September 2003, (IM 2003) Amsterdam. (PDF-file for download)

Some literature on abacuses

1. Books and articles

Crook, Welton J.: Abacus Arithmetic. How to perform some calculations on the Chinese abacus. Palto Alto, California, Pcific Books, 1958
Glade, Heinz / Manteuffel, Karl: Am Anfang stand der Abacus. Aus der Kulturgeschichte der Rechengeräte. Urania-Verlag, Leipzig, Jena, Berlin 1973
Hartmuth, Maximilian: Vom Abakus zum Rechenschieber. (Nachdruck der Ausgabe von 1942). Osnabrück; Otto Zeller, 1968
Hauf, Heinz: Vom Calculus zur Mikroprozessortechnik. In: VDI nachrichten magazin 6/86, S. 30-36 1986 
IBM Deutschland: Computertechnologie: Textbuch und Overhead-Folien über die technische Entwicklung, die zur Computertechnik von heute geführt hat.
Ifrah, Georges: FROM ONE TO ZERO. A Universal History of Numbers. Viking Penguin Inc. New York 1985
Kleiner, Elisabeth / Kradolfer, Peter: Wegmarken der Technikgeschichte, Teil 1. Eine interdisziplinäre Unterrichtseinheit für Französisch, Geschichte, Informatik und Mathematik. Aarau (Schweiz), Verlag Sauerländer, 1996
Kojima, Tagashi: The Japanese Abacus. Its Use and Theory.Tokyo; Charles E. Tuttle Co., Inc. 1954, Thirty-seventh printing 1998.
Kojima, Tagashi: Advanced Abacus - Japanese Theory and Practice. Published by the Charles E. Tuttle Company, Inc. of Rutland, Vermont & Tokyo, Japan, first edition 1963, fourth printing, 1968
Lau Chung Him: The Principles and Practice of the Chinese Abacus. Hong Kong 1958
Menninger, Karl: Kulturgeschichte der Zahlen. Aus der Entwicklung unserer Zahlsprache, unserer Zahlschrift und des Rechenbrettes. Ferdinand Hirt-Verlag, Breslau 1934
Pullan, J.M.: The History of the Abacus. Hutchinson of London 1968
Tani, Yukio: The Magic Calculator - The Way of Abacus. Tokyo; Japan Publications Trading Company, 1973
Tweedale, Geoffrey: Claculating Machines and Computers. Shire Album 247. Buckinghamshire (UK): Shire Publications Ltd 1990
Wie geht das: Abakus. Schwäbisch Hall 1979, Heft 1, S. 2-3
o. V.: The Fundamental Operations in Bead Arithmetic. How to use the Chinese Abacus. Hong Kong o. J.

2. Catalogues and other publications:

Beinhauer, Karl. W. (Hrsg.): Die Sache mit Hand und Fuß - 8000 Jahre Messen und Wiegen. Reiss Museum der Stadt Mannheim, 1994
Erbslöh, Diethard / Rietzke, Ina (Hrsg.): Sonderausstellung "Zahlen, Zählen, Rechenkünste" Museum im Adler, Benningen am Neckar 1999
Faulstich, Peter: Rechen-Technik. Vom Kerbholz zum Computer. Hannoversch Münden 1991 (Dokumentation anlässlich einer Ausstellung der Sparkasse Münden 1991)
Lütjens, Jörn: Traditionelle Rechengeräte - heute noch im Gebrauch. In: Weidauer, Manfred / Stadtverwaltung Erfurt (Hrsg.): Summa Summarum - das macht nach Adam Ries. Ausstellungskatalog des Stadtmuseums "Haus zum Stockfisch", S. 72-75, Erfurt 2002.
Puhle, Matthias (Hrsg.): Von der Erfindung der Zahl zum Computer. Ausstellungskatalog des Kulturhistorischen Museums Magdeburg vom 14.5.92-16.8.92. Magdeburg 1992




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This web site is owned by Prof. Dr. Jörn Lütjens (Hamburg, Germany)

© J. Lütjens, April 2012