Traditional Abacus and Bead Arithmetic/Bibliography

< Traditional Abacus and Bead Arithmetic

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Ancient Chinese books

Sunzi 孫子 (3rd to 5th centuries AD). 孫子算經 (in Chinese). {{cite book}}: Check date values in: |year= (help); Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Zhū Shìjié 朱士傑 (1993) [1299]. Suànxué Qǐméng (算學啟蒙) (in Chinese). Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)
Xú Xīnlǔ (徐心魯) (1993) [1573]. Pánzhū Suànfǎ (盤珠算法) (in Chinese). Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Kē Shàngqiān (柯尚遷) (1993) [1578]. Shùxué Tōngguǐ (數學通軌) (in Chinese). Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Chéng Dàwèi (程大位) (1993) [1592]. Suànfǎ Tǒngzōng (算法統宗) (in Chinese). Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Ancient Japanese books

Mori, Kambei (毛利重能) (1622). Warisansho (割算書) (in Japanese). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Yoshida, Mitsuyoshi (吉田光由) (1634). Jinkoki (塵劫記) (in Japanese). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Momokawa, Jihei (百川治兵衛) (1645). Kamei Zan (亀井算) (in Japanese). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Shinoda, Shosaku (篠田正作) (1895). Jitsuyo Sanjutsu (実用算術) (in Japanese). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Books

Newcomb, Simon (c1882), Logarithmic and other mathematical tables with examples of their use and hints on the art of computation, New York: Henry Holt and Company {{citation}}: Check date values in: |year= (help)

Williams, Samuel Wells; Morrison, John Robert (1856), A Chinese commercial guide, Canton: Printed at the office of the Chinese Repository, p. 298

Smith, David Eugene; Mikami, Yoshio (1914), A history of Japanese mathematics, Chicago: The Open court publishing company

Ang Tian Se; Lam Lay Yong (2004), Fleeting Footsteps; Tracing the Conception of Arithmetic and Algebra in Ancient China (PDF), World Scientific Publishing Company, ISBN 981-238-696-3

Kwa Tak Ming (1922), The Fundamental Operations in Bead Arithmetic, How to Use the Chinese Abacus (PDF), San Francisco: Service Supply Co.

Goded Mur, Antonino (1945), Matemáticas [Mathematics] (in Spanish), Zaragoza (Spain): Compendios CHOP {{citation}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Kojima, Takashi (1954), The Japanese Abacus: its Use and Theory, Tokyo: Charles E. Tuttle Co., Inc., ISBN 978-0-8048-0278-9

Kojima, Takashi (1963), Advanced Abacus: Theory and Practice, Tokyo: Charles E. Tuttle Co., Inc., ISBN 978-0-8048-0003-7

Martzloff, Jean-Claude (2006), A history of chinese mathematics, Springer, ISBN 978-3-540-33782-9

Journal articles and book chapters

Knott, Cargill G. (1886), "The Abacus, in its Historic and Scientific Aspects", Transactions of the Asiatic Society of Japan, 14: 18–73

Goded Mur, Antonino (1945). Matemáticas (in Spanish). Zaragoza (Spain): Compendios CHOP. pp. 20–26. {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

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)". Kokushikan University School of Political Science and Economics (in Japanese). 55 (2). ISSN 0586-9749 – via Kokushikan. {{cite journal}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

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)". Kokushikan University School of Political Science and Economics (in Japanese). 56 (1). ISSN 0586-9749 – via Kokushikan. {{cite journal}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Suzuki, Hisao (鈴木久男) (1982). "Chuugoku ni okeru shuzan kagen-hou 中国における珠算加減法". Kokushikan University School of Political Science and Economics (in Japanese). 57 (3). ISSN 0586-9749 – via Kokushikan. {{cite journal}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Chen, Yifu (2018), "The Education of Abacus Addition in China and Japan Prior to the Early 20th Century", in Volkov, Alexei; Freiman, Viktor (eds.), Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators, Springer Publishing, ISBN 978-3-319-73396-8

Volkov, Alexei (2018), "Visual Representations of Arithmetical Operations Performed with Counting Instruments in Chinese Mathematical Treatises", in Furinghetti, Fulvia; Karp, Alexander (eds.), Researching the History of Mathematics Education - An International Overview, Springer Publishing, ISBN 978-3-319-68293-8

Lisheng Feng (2020), "Traditional Chinese Calculation Method with Abacus", in Jueming Hua; Lisheng Feng (eds.), Thirty Great Inventions of China, Jointly published by Springer Publishing and Elephant Press Co., Ltd, ISBN 978-981-15-6525-0

PhD thesis

Chen, Yifu (2013). 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 (PhD thesis) (in French). Université Paris-Diderot (Paris 7). {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Web articles

"The Definitive Higher Math Guide on Integer Long Division (and Its Variants)". Math Vault. Archived from the original on May 14, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Wilson, Jeff. "Long Division Teaching Aid, "Double Division"". Double Division. Archived from the original on March 02, 2021. {{cite web}}: Check date values in: |archivedate= (help); Text "year 2005" ignored (help); Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Heffelfinger, Totton; Hinkka, Hannu (2011). "The 5 Earth Bead Advantage". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Heffelfinger, Totton; Tejón, Fernando (2005). "Multifactorial Multiplication". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

"割り算九九". Japanese Wikipedia. {{cite web}}: Unknown parameter |Language= ignored (|language= suggested) (help); Unknown parameter |accesdate= ignored (|access-date= suggested) (help); Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

Heffelfinger, Totton (2003). "Square Roots as Solved by Kojima". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Siqueira, Edvaldo; Heffelfinger, Totton. "Kato Fukutaro's Square Roots". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Treadwell, Steve (2015). "Improvements to the Kato Method for Finding Square Roots" (PDF). 算盤 Abacus: Mystery of the Bead. Archived from the original (PDF) on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Baggs, Shane; Heffelfinger, Totton (2011). "Cube Roots". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Heffelfinger, Totton (2013). "Suan Pan and the Unit Rod - Division". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Heffelfinger, Totton (2013). "Short Division Techniques - Chinese Suan Pan". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Heffelfinger, Totton (2013). "Long Division Techniques - Chinese Suan Pan". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Heffelfinger, Totton (2013). "Chinese Division Rules on a Soroban". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Heffelfinger, Totton (2004). "Traditional Multiplication techniques for Chinese Suan Pan - The "Extra Bead" and the "Suspended Bead"". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Heffelfinger, Totton (2013). "Suan Pan and the Unit Rod - Multiplication". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Murakami, Masaaki (2020). "Specially Crafted Division Tables" (PDF). 算盤 Abacus: Mystery of the Bead. Archived from the original (PDF) on August 1, 2021. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Tone? (2017). "Square root and Cube root using Abacus". とね日記. {{cite web}}: Unknown parameter |accesdate= ignored (|access-date= suggested) (help)

Murakami, Masaaki (2020-06-29). "The 5th lower bead". (Web link). Retrieved on 2021-08-13.

Cabrera, Jesús (2021), jccAbacus, retrieved 4 August 2021

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