Traditional Abacus and Bead Arithmetic/Bibliography

< Traditional Abacus and Bead Arithmetic

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