Traditional Abacus and Bead Arithmetic/Bibliography
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Ancient Chinese books
[edit | edit source]- Sunzi 孫子 (3rd to 5th centuries AD). 孫子算經 (in Chinese).
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- 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).
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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).
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- 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).
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- 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).
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Ancient Japanese books
[edit | edit source]- Mori, Kambei (毛利重能) (1622). Warisansho (割算書) (in Japanese).
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- Yoshida, Mitsuyoshi (吉田光由) (1634). Jinkoki (塵劫記) (in Japanese).
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- Momokawa, Jihei (百川治兵衛) (1645). Kamei Zan (亀井算) (in Japanese).
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- Shinoda, Shosaku (篠田正作) (1895). Jitsuyo Sanjutsu (実用算術) (in Japanese).
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Books
[edit | edit source]- 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
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- 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
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- 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
[edit | edit source]- 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.
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- 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.
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- 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.
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- 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.
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- 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
[edit | edit source]- 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).
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Web articles
[edit | edit source]- "The Definitive Higher Math Guide on Integer Long Division (and Its Variants)". Math Vault. Archived from the original on May 14, 2021.
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- Wilson, Jeff. "Long Division Teaching Aid, "Double Division"". Double Division. Archived from the original on March 02, 2021.
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- 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.
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- Heffelfinger, Totton; Tejón, Fernando (2005). "Multifactorial Multiplication". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021.
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- "割り算九九". Japanese Wikipedia.
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- Heffelfinger, Totton (2003). "Square Roots as Solved by Kojima". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021.
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- Siqueira, Edvaldo; Heffelfinger, Totton. "Kato Fukutaro's Square Roots". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021.
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- 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.
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- Baggs, Shane; Heffelfinger, Totton (2011). "Cube Roots". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 1, 2021.
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- 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.
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- Heffelfinger, Totton (2013). "Short Division Techniques - Chinese Suan Pan". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021.
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- Heffelfinger, Totton (2013). "Long Division Techniques - Chinese Suan Pan". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021.
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- Heffelfinger, Totton (2013). "Chinese Division Rules on a Soroban". 算盤 Abacus: Mystery of the Bead. Archived from the original on August 3, 2021.
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- 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.
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- 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.
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- Murakami, Masaaki (2020). "Specially Crafted Division Tables" (PDF). 算盤 Abacus: Mystery of the Bead. Archived from the original (PDF) on August 1, 2021.
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- Tone? (2017). "Square root and Cube root using Abacus". とね日記.
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- Murakami, Masaaki (2020-06-29). "The 5th lower bead". (Web link). Retrieved on 2021-08-13.
- Cabrera, Jesús (2021), jccAbacus, retrieved 4 August 2021