411 REFERENCE · Wikibooks
Traditional Abacus and Bead Arithmetic/Bibliography
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Ancient Chinese books
Sunzi 孫子
孫子算經
Master Sun's Mathematical Manual
3rd to 5th centuries AD
Chinese
https://zh.wikisource.org/wiki/%E5%AD%AB%E5%AD%90%E7%AE%97%E7%B6%93
Zhū Shìjié 朱士傑
Suànxué Qǐméng (算學啟蒙)
Mathematical Illustration
1299
1993
Chinese
Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙)
Xú Xīnlǔ (徐心魯)
Pánzhū Suànfǎ (盤珠算法)
Computational Methods with the Beads in a Tray
1573
1993
Chinese
Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙)
Kē Shàngqiān (柯尚遷)
Shùxué Tōngguǐ (數學通軌)
Mathematical Track
1578
1993
Chinese
Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙)
Chéng Dàwèi (程大位)
Cheng Dawei
Suànfǎ Tǒngzōng (算法統宗)
General Source of Computational Methods
1592
1993
Chinese
Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙)
Ancient Japanese books
Mori, Kambei (毛利重能)
Warisansho (割算書)
Division Book
1622
Japanese
https://archive.wul.waseda.ac.jp/kosho/i16/i16_00001/i16_00001.html
Yoshida, Mitsuyoshi (吉田光由)
Jinkoki (塵劫記)
Dust Record
1634
Japanese
https://dl.ndl.go.jp/info:ndljp/pid/3508170/7
Momokawa, Jihei (百川治兵衛)
Kamei Zan (亀井算)
Kamei's Arithmetics
1645
Japanese http://base1.nijl.ac.jp/iview/Frame.jsp?DB_ID=G0003917KTM&C_CODE=THKW-06252&IMG_SIZE=&PROC_TYPE=null&SHOMEI=%E3%80%90%E4%BA%80%E4%BA%95%E7%AE%97%E3%80%91&REQUEST_MARK=null&OWNER=null&BID=null&IMG_NO=1
Shinoda, Shosaku (篠田正作)
Jitsuyo Sanjutsu (実用算術)
Practical Arithmetics
1895
Japanese https://dl.ndl.go.jp/info:ndljp/pid/827128/5?tocOpened=1&itemId=info%3Andljp%2Fpid%2F827128&contentNo=5&__lang=en
Books
Newcomb, Simon
Logarithmic and other mathematical tables with examples of their use and hints on the art of computation
New York
c. 1882
Henry Holt and Company
https://archive.org/details/logarithmicother00newcrich/page/n5/mode/2up
Williams, Samuel Wells
Morrison, John Robert
A Chinese commercial guide
1856
Canton: Printed at the office of the Chinese Repository
https://archive.org/details/chinesecommercia00willuoft/page/298/mode/2up
298
Smith, David Eugene
Mikami, Yoshio
A history of Japanese mathematics
Chicago
1914
The Open court publishing company
https://archive.org/details/historyofjapanes00smitiala/page/42/mode/2up
Ang Tian Se
Lam Lay Yong
Lam Lay Yong
Fleeting Footsteps; Tracing the Conception of Arithmetic and Algebra in Ancient China
2004
World Scientific Publishing Company
981-238-696-3
https://www.worldscientific.com/doi/suppl/10.1142/5425/suppl_file/5425_chap1.pdf
Kwa Tak Ming
The Fundamental Operations in Bead Arithmetic, How to Use the Chinese Abacus
San Francisco
1922
Service Supply Co.
https://archive.computerhistory.org/resources/access/text/2016/12/B1671.01-05-01-acc.pdf
PDF
Goded Mur
Antonino
Matemáticas [Mathematics]
Mathematics
Spanish
Zaragoza (Spain)
1945
Compendios CHOP
The Japanese Abacus: its Use and Theory
Kojima
Takashi
1954
Charles E. Tuttle Co., Inc.
Tokyo
978-0-8048-0278-9
https://archive.org/details/japaneseabacus00taka
Advanced Abacus: Theory and Practice
Kojima
Takashi
1963
Charles E. Tuttle Co., Inc.
Tokyo
978-0-8048-0003-7
A history of chinese mathematics
Martzloff
Jean-Claude
2006
Springer
978-3-540-33782-9
Journal articles and book chapters
Knott, Cargill G.
The Abacus, in its Historic and Scientific Aspects
Transactions of the Asiatic Society of Japan
14
1886
18-73
https://archive.org/details/in.gov.ignca.26020/page/17/mode/2up
Goded Mur, Antonino
Matemáticas
Spanish
Mathematics
Zaragoza (Spain)
1945
Compendios CHOP
20-26
Suzuki, Hisao (鈴木 久男)
1980
Chūgoku ni okeru josan-hō no kigen (1 ) 中国における除算法の起源(1)
Origin of Division Method in China (1) https://kokushikan.repo.nii.ac.jp/?action=pages_view_main&active_action=repository_view_main_item_detail&item_id=8365&item_no=1&page_id=13&block_id=21
Kokushikan University School of Political Science and Economics
Japanese
55
2
Kokushikan
0586-9749
Suzuki, Hisao (鈴木 久男)
1981
Chūgoku ni okeru josan-hō no kigen (2 ) 中国における除算法の起源(2)
Origin of Division Method in China (2) https://kokushikan.repo.nii.ac.jp/?action=pages_view_main&active_action=repository_view_main_item_detail&item_id=8365&item_no=1&page_id=13&block_id=21
Kokushikan University School of Political Science and Economics
Japanese
56
1
Kokushikan
0586-9749
Suzuki, Hisao (鈴木 久男)
1982
Chuugoku ni okeru shuzan kagen-hou 中国における珠算加減法
Abacus addition and subtraction methods in China
http://id.nii.ac.jp/1410/00008407/
Kokushikan University School of Political Science and Economics
Japanese
57
3
Kokushikan
0586-9749
Chen
Yifu
The Education of Abacus Addition in China and Japan Prior to the Early 20th Century
Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators
Springer Publishing
2018
https://link.springer.com/book/10.1007%2F978-3-319-73396-8
978-3-319-73396-8
Volkov, Alexei
Freiman, Viktor
Volkov
Alexei
Visual Representations of Arithmetical Operations Performed with Counting Instruments in Chinese Mathematical Treatises
Researching the History of Mathematics Education - An International Overview
Springer Publishing
2018
https://www.springer.com/gp/book/9783319682938
978-3-319-68293-8
Furinghetti, Fulvia
Karp, Alexander
Lisheng Feng
Traditional Chinese Calculation Method with Abacus
Thirty Great Inventions of China
Jointly published by Springer Publishing and Elephant Press Co., Ltd
2020
https://link.springer.com/book/10.1007%2F978-981-15-6525-0
978-981-15-6525-0
Jueming Hua
Lisheng Feng
PhD thesis
Chen
Yifu
L’étude des Différents Modes de Déplacement des Boules du Boulier et de l’Invention de la Méthode de Multiplication Kongpan Qianchengfa et son Lien avec le Calcul Mental
The Study of the Different Modes of Movement of the Abacus Beads and the Invention of the Kongpan Qianchengfa Multiplication Method and its Link with Mental Calculation
PhD thesis
2013
French
Université Paris-Diderot (Paris 7)
http://www.theses.fr/2013PA070061
Web articles
The Definitive Higher Math Guide on Integer Long Division (and Its Variants)
Math Vault
https://mathvault.ca/long-division/
August 4, 2021
https://web.archive.org/web/20210514014622/https://mathvault.ca/long-division/
May 14, 2021
Long Division Teaching Aid, "Double Division"
Double Division
2005
Wilson, Jeff
http://www.doubledivision.org/
September 26, 2021
https://web.archive.org/web/20210302073004/http://www.doubledivision.org/
March 2, 2021
The 5 Earth Bead Advantage
2011
Heffelfinger, Totton
Hinkka, Hannu
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/soroban/Hannu/5_Bead/
August 9, 2021
https://web.archive.org/web/20210801083504/http://totton.idirect.com/soroban/Hannu/5_Bead/
August 1, 2021
Multifactorial Multiplication
2005
Heffelfinger, Totton
Tejón, Fernando
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/soroban/MultiFac/
August 14, 2021
https://web.archive.org/web/20210801083254/http://totton.idirect.com/soroban/MultiFac/
August 1, 2021
割り算九九
Division table
Japanese Wikipedia
Japanese
https://ja.wikipedia.org/wiki/%E4%B9%9D%E4%B9%9D#%E5%89%B2%E3%82%8A%E7%AE%97%E4%B9%9D%E4%B9%9D
August 11, 2021
Square Roots as Solved by Kojima
2003
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/soroban/KojimaSq/
August 16, 2021
https://web.archive.org/web/20210801083034/http://totton.idirect.com/soroban/KojimaSq/
August 1, 2021
Kato Fukutaro's Square Roots
Siqueira, Edvaldo
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/soroban/katoSq/
August 10, 2021
https://web.archive.org/web/20210801083040/http://totton.idirect.com/soroban/katoSq/
August 1, 2021
Improvements to the Kato Method for Finding Square Roots
2015
Treadwell, Steve
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/soroban/Steve%20Treadwell/Improvements_to_the_Kato_Square_Root_Method.pdf
August 10, 2021 https://web.archive.org/web/20210801083500/http://totton.idirect.com/soroban/Steve%20Treadwell/Improvements_to_the_Kato_Square_Root_Method.pdf
August 1, 2021
Cube Roots
2011
Baggs, Shane
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/soroban/Hannu/5_Bead/
August 9, 2021
https://web.archive.org/web/20210801083517/http://totton.idirect.com/soroban/Cube_Root/
August 1, 2021
Suan Pan and the Unit Rod - Division
2013
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/suanpan/shiftDivision/
August 4, 2021
https://web.archive.org/web/20210803045740/http://totton.idirect.com/suanpan/shiftDivision/
August 3, 2021
Short Division Techniques - Chinese Suan Pan
2013
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/suanpan/sh_div/
August 4, 2021
https://web.archive.org/web/20210803045740/http://totton.idirect.com/suanpan/sh_div/
August 3, 2021
Long Division Techniques - Chinese Suan Pan
2013
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/suanpan/long_div/
August 4, 2021
https://web.archive.org/web/20210803045739/http://totton.idirect.com/suanpan/long_div/
August 3, 2021
Chinese Division Rules on a Soroban
2013
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/soroban/Ch_Rule_Soroban/
August 4, 2021
https://web.archive.org/web/20210803045741/http://totton.idirect.com/soroban/Ch_Rule_Soroban/
August 3, 2021
Traditional Multiplication techniques for Chinese Suan Pan - The "Extra Bead" and the "Suspended Bead"
2004
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/suanpan/
August 7, 2021
https://web.archive.org/web/20210801083036/http://totton.idirect.com/suanpan/
August 1, 2021
Suan Pan and the Unit Rod - Multiplication
2013
Heffelfinger, Totton
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/suanpan/shiftMultiplication/
August 7, 2021
https://web.archive.org/web/20210801083439/http://totton.idirect.com/suanpan/shiftMultiplication/
August 1, 2021
Specially Crafted Division Tables
2020
Murakami, Masaaki
算盤 Abacus: Mystery of the Bead
http://totton.idirect.com/soroban/masaaki/Specially%20Crafted%20Division%20Tables.pdf
PDF
August 13, 2021
https://web.archive.org/web/20210801083501/http://totton.idirect.com/soroban/masaaki/Specially%20Crafted%20Division%20Tables.pdf
August 1, 2021
Square root and Cube root using Abacus
2017
Tone?
とね日記
https://blog.goo.ne.jp/ktonegaw/e/f62fb31b6a3a0417ec5d33591249451b
August 17, 2021
Murakami, Masaaki
The 5th lower bead
2020-06-29
https://groups.io/g/sorobanabacus/message/562
2021-08-13
https://jccabacus.blogspot.com
jccAbacus
Cabrera
Jesús
2021
4 August 2021
Appendix: Abbreviated operations