有關古代中國數學史的學術論文，大多數集中於對中國算書內所提供的解決數學問題的算法的解釋. 然而, 我在這篇論文中的研究, 並不意欲繼續這一研究方向，而是集中於中國算書內的圖，及這些圖在數學文本中的應用。
為了解決我對中國數學圖的研究問題，我將在本論文的章節中, 將中國算書的數學圖形作分類，例如直角三角形的圖、面積形狀和大小、平方根提取和遠程測量。並討論各個”數學圖形”在不同數學家及不同時代下有何異同。我希望所提出的研究能更好好地理解中國古代數學書籍中各種圖表的變化及其背後可能的成因，並提供一致的描述。 最後，我將嘗試說明圖表在東方中國和日本數學中的作用和使用。

Most scholarly papers on the history of mathematics in China focus on the interpretation of algorithms provided in them for solution of mathematical problems; my research in this thesis does not continue this line of studies, but instead focuses on the diagrams, tu 圖, and their application in mathematical texts.
In order to address my research question on diagrams in Chinese mathematics, I would like to list below the projected chapters of my thesis and discuss the individual diagram types, for example the diagrams of right-angle triangle, area shape and size, square root extraction and remote surveying. I hope that the proposed research will give me a better understanding of the changing of various diagrams in ancient Chinese mathematics books and provide consistent descriptions. Finally, I will try to illustrate the role and use of diagrams in Chinese and Japanese mathematics in the East.

Primary Materials:

 1. An Zhizhai 安止齋, Xiangming suanfa 《詳明算法》, Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
2. Cheng Dawei 程大位, Suanfa tongzong 《算法統宗》,Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan II 中國科學技術典籍通彙.數學卷二). Zhengzhou: Henan jiaoyu chubanshe, 1993.
3. Clavius, C. Euclidis Elementorum Libri XV, Rome: Apud Camillum Francischinum,1574.
4. Jia Heng 賈亨, Suanfa quanneng ji 《算法全能集》, Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
5. Li Ye 李冶, Ceyuan haijing 《測圓海鏡》, Zhibuzu zhai congshu (知不足齋叢書, Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993
6. Li Ye 李冶, Yigu yan duan 《益古演段》, Zhibuzu zhai congshu (知不足齋叢書), Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
7. Liu Hui 劉徽 (commentator), Jiuzhang suanshu zhu 《九章算術》, Wuyingdian juzhenban congshu (武英殿聚珍版叢書), Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
8. Qin Jiushao 秦九韶, Shushu Jiuzhang 《數書九章》, Yijiatang congshu宜稼堂叢書), Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
9. Ricci, Matteo and Xu Guangqi 利瑪竇,徐光啟, Jihe yuanben 《幾何原本》, Qinding Siku Quanshu, Zi bu 6 欽定四庫全書 子部六, edition of preserving in Zhejiang University Library 浙江大學圖書館.
10. Wang Wensu 王文素, Suanxue baojian 《算學寶鑑》,Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan II 中國科學技術典籍通彙.數學卷二). Zhengzhou: Henan jiaoyu chubanshe, 1993.
11. Wu Jing 吳敬, Jiuzhang suanfa bilei daquan《九章算法比類大全》,Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan II 中國科學技術典籍通彙.數學卷二). Zhengzhou: Henan jiaoyu chubanshe, 1993.
12. Yang Hui 楊輝, Xiangjie jiuzhang suan fa 《詳解九章算法》, Yijiatang congshu 宜稼堂叢書, Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
13. Yang Hui 楊輝, Yang Hui suanfa 《楊輝算法》, Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
14. Yongle dadian suanfa, 《永樂大典算法》, Collection of Chinese science and technology classics. Mathematics volumes (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
15. Yoshida Mitsuyoshi 吉田光由, Jinkōki 塵劫記, photo-reproduction of the editions of 1627 and 1631, Kyoto University Library.
16. Zhao Junqing 趙君卿 (commentator), Zhoubi Suanjing《周髀算經》, Wuyingdian juzhenban congshu (武英殿聚珍版叢書), Collection of Chinese science and technology classics. Mathematics volume (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.
17. Zhu Shijie 朱世傑, Suanxue qimeng《算學啟蒙》, Luo Shilin's proofreading, photocopy of Yangzhou engraved copy (羅士琳校勘揚州刻本影印), Collection of Chinese science and technology classics. Mathematics volume (Zhongguo kexue jishu dianji tonghui. Shuxue juan I 中國科學技術典籍通彙.數學卷一). Zhengzhou: Henan jiaoyu chubanshe, 1993.

Translations of Primary Materials and Secondary Publications:

1. Bull, Rebecca; Lee Kerry (2014). “Executive Functioning and Mathematics Achievement “Child development perspectives, Vol.8 (1), p.36-41, Article 36.
2. Chen Shaofeng陳少峰 (2001), song ming li xue yu dao jia zhe xue《宋明理學與道家哲學》Neo Confucianism and Taoist Philosophy in Song and Ming Dynasties, Shanghai: Shanghai Culture Press, 2001.
3. Chemla, Karine and Guo Shuchun (2004), 九章算術 LES NEUF CHAPITRES, Paris: Dunod Press.
4. Chemla, Karine (2010). Changes and Continuities in the Use of Diagrams Tu in Chinese Mathematical Writings (Third Century to Fourteenth Century I), East Asian Science, Technology and Society: an International Journal vol. 4, no. 2 (2010), pp. 303–326; available online at https://www.researchgate.net/publication/248142774_Changes_and_Continuities_in_the_Use_of_Diagrams_Tu_in_Chinese_Mathematical_Writings_Third_Century_to_Fourteenth_Century_I.
5. Chemla, Karine (2005). Geometrical figures and generality in ancient China and beyond: Liu Hui and Zhao Shuang, Plato and Thabit ibn Qurra. Science in Context, 18, 123–166.
6. Chemla 林力娜, K., Ma 馬彪, B. (2020). The Use of Volume in the Measurement of Grain in Early Imperial China. In: Michel, C., Chemla, K. (eds) Mathematics, Administrative and Economic Activities in Ancient Worlds. Why the Sciences of the Ancient World Matter, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-48389-0_7
7. Chen Liangtso 陳良佐. Zhao Shuang gougu yuanfang tu zhu zhi yanjiu 趙爽勾股圓方圖注之研究 (Research on Zhao Shuang's Commentaries on the diagrams of Right-Angled Triangles and of Circle and Square), Dalu zazhi 大陸雜誌 (Mainland China Magazine), vol. 1, 1982, pp. 33-52.
8. Cullen, Christopher (1996). Astronomy and mathematics in ancient China: The Zhou bi suan jing. Cambridge [England] and New York: Cambridge University Press.
9. Cullen, Christopher (2004). The Suàn shù shū 筭數書 ‘Writings on reckoning’: A translation of a Chinese mathematical collection of the second century BC, with explanatory commentary. Cambridge (UK): Needham Research Institute.
10. Guo Jinbin郭金彬, On the History of Traditional Chinese Scientific Thought 《中國傳統科學思想史論 》Zhongguo chuantong kexue sixiang shilun, Beijing: Zhishi Press.
11. Guo Shuchun 郭書春 (1993). Zhongguo kexue jishu dianji tonghui. Shuxue juan 中國科學技術典籍通彙.數學卷. Zhengzhou: Henan jiaoyu chubanshe.
12. Guo Shuchun 郭書春 (1995), Zhongguo gudai shuxue 《中國古代數學》Ancient Chinese Mathematics, Taipei: Taiwan Business Press.
13. Guo Shuchun 郭書春 (2012), Zhongguo chuantong shuxue shihua《中國傳統數學史話》History of Traditional Chinese Mathematics, Beijing: China International Radio Press,
14. Hua Luogeng (2018), Daizai shuxue zhi wei yong: Hua Luogeng kepu zhuzuo xuanji《大哉數學之為用: 華羅庚科普著作選集》Great Mathematics for Use: An Anthology of Hua Luogeng's Science Works, Shanghai Education Press.
15. Horng Wann-Sheng 洪萬生(2000), Suanshushu chu tan《算數書》初探, A Preliminary Study of the "Suan Shu Shu", Journal of Taiwan Normal University: Science Education, vol. 45, no. 2, pp. 77-90. doi:10.6300/JNTNU.2000.45(2).05.
16. Horng Wann-Sheng 洪萬生 (2002), shiba shiji dongsuan yu zhongsuan de yiduan duihua; Hong Zhengxai vs. He guozhu 十八世紀東算與中算的一段對話：洪正夏vs.何國柱, A Dialogue Between Korean and Chinese Mathematics in the 18th Century: Hong Zhengxia vs. He Guozhu, Chinese Studies, vol 20 (2), pp. 57-80.
17. Horng Wann-Sheng 洪萬生, Li Chien-Tsung 李建宗 (2007), cong dongsuan shushi Qing shanzheng kan shiqi shiji chaoxian Yichang shuxue yantaohui 從東算術士慶善徵看十七世紀朝鮮一場數學研討會 Kyong Song-jin and a Mathematics Workshop in 17th Century Choson Korea, Chinese Studies, vol 25(1), 313-340, doi:10.6770/CS.2007.
18. Hu Shi 胡適(1919), Zhongguo zhexueshi dagang 《中國哲學史大綱》Outline of the History of Chinese Philosophy, ShangHai: Commercial Press, reprinted in 1925, p.144-253.
19. Hu Shih 胡適 (1922). The Development of the Logical Method in Ancient China. Shanghai: The Oriental Book Company.
20. Johnston, Ian (2009). The Mozi: A Complete Translation. Hong Kong: The Chinese University Press.
21. Kong Guoping孔國平 (1992), Song yuan shiqi de zhexue yu shuxue宋元時期的哲學與數學 Philosophy and Mathematics in the Song and Yuan Dynasties. Collected in 《中國科學技術史國際學術討論會論文集, 北京, 1990》International Symposium on the History of Science and Technology in China, Beijing 1990, Beijing: China Science and Technology Press.
22. Lam Lay Yong. (1977). A critical study of the Yang Hui suan fa. A thirteenth-century Chinese mathematical treatise. Singapore: Singapore University Press.
23. Lao Hansheng勞漢生 (2000) , Zhusuan yu shiyong suanshu 《珠算與實用算術》Abacus and Practical Arithmetic, Shijiazhuang City: Hebei Technology Press.
24. Li Jimin 李繼閔 (1986), Shilun zhongguo chuangtong shuxue de tedian 試論中國傳統數學的特點 On the Characteristics of Chinese Traditional Mathematics, Essays on the History of Chinese Mathematics II 《中國數學史論文集 二》, Jinan: Shandong Education Press.
25. Li Jimin 李繼閔 (1993). Shang Gao dingli bianzheng 商高定理辨證 Dialectics of Shang Gao Theorem, Studies in the History of Natural Science 自然科學史研究, vol.12. No.1, p.29-41.
26. Li Jimin李繼閔 (2020), Shi gua fa wei shutan蓍卦發微初探A preliminary Exploration of shi gua fa wei. Collected in 《zhaongguo gudai shuxuejia Qin Jiuzhao yu shushu jiuzhang yanjiu中國古代數學家秦九韶與《數書九章》研究》, The study of Qin Jiushao, an ancient Chinese mathematician and Shushu jiuzhang, Haerbin: Harbin Institute of Technology Press.
27. Libbrecht, Ulrich (1973). Chinese mathematics in the thirteenth century: The Shu-shu Chiu-Chang of Ch'in Chiu-Shao. Cambridge, Mass: MIT Press.
28. Li Yan李儼 (1977), Cong zhongguo suanxueshi shang kan zhong chao wenhua jiaoliu 從中國算學史上看中朝文化交流 (Viewing the Cultural Exchange between China and Korea from the History of Chinese Mathematics), 《中算史論叢》(Collected works on the History of Chinese Mathematics), Taipei: Taiwan Business Press, vol. 5, pp. 559-563.
29. Li Yan 李儼 (1977), Zhongsuan shuru riben de jingguo中算輸入日本的經過 (The process of introduction of Chinese mathematics to Japan), 《中算史論叢》 (Collected works on the History of Chinese Mathematics), Taipei: Taiwan Business Press, vol. 5, pp.168-186.
30. Li, Y., & Geary, D. C. (2017). Children's visuospatial memory predicts mathematics achievement through early adolescence. PLoS ONE, 12(2), Article e0172046.
31. Liang Zongju梁宗巨 (1983), Cong shuxueshi kan zhongguo jindai kexue luohou de yuanyin 從數學史看中國近代科學落後的原因Cause of the Backwardness of China’s Modern Science Viewed from the History of Mathematics. Collection of Tradition and Culture of Science 《科學傳統與文化》, Xi'an: Shanxi Science and Technology Press, p.250-266.
32. Li Peiye 李培業 (2007), Zhongguo zhusuan jianshi《中國珠算簡史》A Brief History of Chinese Abacus, Beijing: Chinese financial & Economic Publishing House.
33. Martzloff, Jean-Claude (1997). A History of Chinese Mathematics, Springer.
34. Needham, Joseph (1954-1959). Science and Civilization in China. Cambridge: Cambridge University Press.
35. Netz, Reviel (1999). The shaping of deduction in Greek mathematics: A study in cognitive history. Cambridge University Press.
36. Ogura Kinnosuke小倉金之助 (1938), 中国数学の特殊性 The Peculiarities of Chinese Mathematics, Mathematical History Research Volume 2, Tokyo: Iwanami Press.
37. Pollet, Charlotte, and Ying, Jia-Ming (2017), One quadratic equation, different understandings: the 13th century interpretations by Li Ye and later commentaries in the 18th and 19th centuries, Journal for History of Mathematics, 30, pp. 137-162.
38. Pollet, Charlotte Victorine (2020). The procedure of the Section of Pieces of Areas in Li Ye and Yang Hui's works: genealogy of diagrams and equations. Science in Context, vol. 33, no.1, pp. 37-63.
39. Qian Baocong 錢寶琮 (1932), Zhongguo suanxueshi《中國算學史》Chinese Mathematics History Volume I, , Beijing: Institute of History and Language, Academia Sinica.
40. Qin Baocong錢寶琮 (1966 ). songyuan shiqi shuxue yu daoxue de guanxi《宋元時期數學與道學的關係》The Relationship between Mathematics and Taoism in the Song and Yuan Dynasties, A Collection of Essays on the History of Mathematics in the Song and Yuan Dynasties《宋元數學史論文集songyuan shuxueshi lunwenji》, Beijing: Science Publisher, p.255.
41. Qian Baocong 錢寶琮 (2019), Zhongguo shuxue shi《中國數學史》History of Chinese Mathematics., Shanghai: Commercial Press.
42. Qu Anjing曲安京 (2002), Zhoubi suanjing xinyi《周髀算經》新議, A new discussion on Zhoubi suangjing, Shanxi: People Press.
43. Research and Conservation Center for Unearthed Texts, Tsinghua University, Warring States Bamboo Slips Collected by Tsinghua University (4), Shanghai: Zhongxi Book Company, 2013.
44. Saito, Ken (2018). Diagrams in the Arithmetical Books of Euclid's Elements. SCIAMVS, vol.19, pp. 103-166,
45. Volkov, Alexei (1996–1997). The mathematical work of Zhao Youqin: remote surveying and the computation of pi. Taiwanese Journal for Philosophy and History of Science, no. 8 (vol. 5, no. 1), pp. 129–189.
46. Volkov, Alexei (2007). Geometrical Diagrams in Liu Hui’s Commentary on the Jiuzhang suanshu. In F. Bray, V. Dorofeeva-Lichtmann, G. Métailié (eds.), Graphics and Text in the Production of Technical Knowledge in China. The Warp and the Weft (Sinica Leidensia 79), Leiden: Brill, pp. 425-459.
47. Volkov, Alexei (2018). Visual representations of arithmetical operations performed with counting instruments in Chinese mathematical treatises. In: Fulvia Furinghetti and Alexander Karp (Eds.), Researching the History of Mathematics Education: An International Overview (ICME-13 Monographs). Cham: Springer, pp. 279–304.
48. Volkov, Alexei (2018). Chinese Counting Rods: Their History, Arithmetic Operations, and Didactic Repercussions. In: Mathematics Education in the Digital Era. Cham: Springer, pp.137 – 188.
49. Ying, Jia-Ming & Su, Yi-Wen (2019). A study on geometrical diagrams for 3-D objects in pre-modern East-Asian mathematical texts. RIMS Kôkyûroku Bessatsu B71,pp. 39-56.
50. Yoshio Mikami三上義夫 (1929), Features of Chinese Mathematics《中國算學之特色》,Translator: Lin Ketang林科棠, Beijing: Business Press.
51. Zhou Xiaohan 周霄漢(2020), Preliminary Research on the Mathematical Methods and Order of Problems in the “Fangcheng” Chapter of Yang Hui’s Mathematical Methods (1261 CE), Chinese Annals of History of Science and Technology 4 (1), 001–062.

Doctoral Theses (Supervisor: Dr. Horng Wann-Sheng)

1. 英家銘Ying, Jia-Ming, (Nam Byeong-gil 1820-1869) Reinterpretation of Classical Mathematics 南秉吉(1820-1869)對古典算學的重新詮釋, Taiwan: National Normal University, PHD thesis, 2009.
2. 博佳佳Pollet, Charlotte Victorine, Exploring the Features of Algebra in Medieval China: the Case of Yigu yanduan, Taiwan: National Normal University, PHD thesis, 2012.