Traditional Abacus and Bead Arithmetic/Bibliography

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