Traditional Abacus and Bead Arithmetic/Bibliography

Ancient Chinese books

• Sunzi 孫子 (3rd to 5th centuries AD). 孫子算經 [Master Sun's Mathematical Manual] (in Chinese). {{cite book}}: Check date values in: |year= (help)

• Zhū Shìjié 朱士傑 (1993) [1299]. Suànxué Qǐméng (算學啟蒙) [Mathematical Illustration] (in Chinese). Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙).
• Xú Xīnlǔ (徐心魯) (1993) [1573]. Pánzhū Suànfǎ (盤珠算法) [Computational Methods with the Beads in a Tray] (in Chinese). Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙).

• Kē Shàngqiān (柯尚遷) (1993) [1578]. Shùxué Tōngguǐ (數學通軌) [Mathematical Track] (in Chinese). Zhōngguó kēxué jìshù diǎnjí tōng huì (中國科學技術典籍通彙).

• Chéng Dàwèi (程大位) (1993) [1592]. Suànfǎ Tǒngzōng (算法統宗) [General Source of Computational Methods] (in 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) (1622). Warisansho (割算書) [Division Book] (in Japanese).

• Yoshida, Mitsuyoshi (吉田光由) (1634). Jinkoki (塵劫記) [Dust Record] (in Japanese).

• Momokawa, Jihei (百川治兵衛) (1645). Kamei Zan (亀井算) [Kamei's Arithmetics] (in Japanese).

• Shinoda, Shosaku (篠田正作) (1895). Jitsuyo Sanjutsu (実用算術) [Practical Arithmetics] (in Japanese).

Books

• Newcomb, Simon (c. 1882), Logarithmic and other mathematical tables with examples of their use and hints on the art of computation, New York: Henry Holt and Company

• 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] [Mathematics] (in Spanish), Zaragoza (Spain): Compendios CHOP

• 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 [Mathematics] (in Spanish). Zaragoza (Spain): Compendios CHOP. pp. 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)]. Kokushikan University School of Political Science and Economics (in Japanese). 55 (2). ISSN 0586-9749 – via Kokushikan.

• 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)]. Kokushikan University School of Political Science and Economics (in Japanese). 56 (1). ISSN 0586-9749 – via Kokushikan.

• 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]. Kokushikan University School of Political Science and Economics (in Japanese). 57 (3). ISSN 0586-9749 – via Kokushikan.

• 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 [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) (in French). Université Paris-Diderot (Paris 7).

Web articles

• "The Definitive Higher Math Guide on Integer Long Division (and Its Variants)". Math Vault. Archived from the original on May 14, 2021. Retrieved August 4, 2021.

• Wilson, Jeff (2005). "Long Division Teaching Aid, "Double Division"". Double Division. Archived from the original on March 2, 2021. Retrieved September 26, 2021.

• 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. Retrieved August 9, 2021.

• Heffelfinger, Totton; Tejón, Fernando (2005). "Multifactorial Multiplication". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. Retrieved August 14, 2021.

• "割り算九九" [Division table]. Japanese Wikipedia (in Japanese). Retrieved August 11, 2021.

• Heffelfinger, Totton (2003). "Square Roots as Solved by Kojima". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. Retrieved August 16, 2021.

• Siqueira, Edvaldo; Heffelfinger, Totton. "Kato Fukutaro's Square Roots". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. Retrieved August 10, 2021.

• 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. Retrieved August 10, 2021.

• Baggs, Shane; Heffelfinger, Totton (2011). "Cube Roots". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021. Retrieved August 9, 2021.

• 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. Retrieved August 4, 2021.

• Heffelfinger, Totton (2013). "Short Division Techniques - Chinese Suan Pan". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021. Retrieved August 4, 2021.

• Heffelfinger, Totton (2013). "Long Division Techniques - Chinese Suan Pan". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021. Retrieved August 4, 2021.

• Heffelfinger, Totton (2013). "Chinese Division Rules on a Soroban". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021. Retrieved August 4, 2021.

• 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. Retrieved August 7, 2021.

• 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. Retrieved August 7, 2021.

• Murakami, Masaaki (2020). "Specially Crafted Division Tables" (PDF). 算盤 Abacus: Mystery of the Bead. Archived from the original (PDF) on August 1, 2021. Retrieved August 13, 2021.

• Tone? (2017). "Square root and Cube root using Abacus". とね日記. Retrieved August 17, 2021.

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

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