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- Yigu_yanduan abstract "Yigu yanduan (益古演段 old mathematics in expanded sections) is a 13th-century mathematical work by Yuan dynasty mathematician Li Zhi. Yigu yanduan was based on North Song mathematician Jiang Zhou (蒋周) Yigu Ji (益古集 Collection of Old Mathematics)which was extinct. However from fragments quoted in Yang Hui's work The Complete Algorithms of Acreage(田亩比类算法大全), we know that this lost mathematical treatise Yigu Ji was about solving area problems with geometry. Li Zhi used the examples of Yigu Ji to introduce the art of Tian yuan shu to new comers to this field. Although Li Zhi's previous monograph Ceyuan haijing also used tian yuan shu, however it is harder to understand than Yigu yanduan.Yigu yanduan was later collected into Siku Quanshu.Yigu yanduan consists of three volumes with 64 problems solved with Tian yuan shu in parallel with geometrical method. Li Zhi intended to introduced students to the art of Tian yuan shu thru ancient geometry. Yigu yanduan together with Ceyuan haijing are considered major contribution to Tian yuan shu by Li Zhi. These two works are also considered as the earliest extant documents on Tian yuans shu.All the 64 problems followed more or less the same format, it started with a question(问), followed by an answer(答曰), a diagram, then an algorithm(术), in which Li Zhi explained step by step how to set up algebra equation with Tian yuan shu, then followed by geometrical interpretation (Tiao duan shu). The order of arrangement of Tian yuan shu equation in Yigu yanduan is the reverse of that in Ceyuan haijing, i.e., here with the constant term at top, followed by first order tian yuan, second order tian yuan, third order tian yuan etc. This later arrangement conformed with contemporary convention of algebra equation( for instance, Qin Jiushao's Mathematical Treatise in Nine Sections), and later became a norm.Yigu yanduan was first introduced to the western world by the British Protestant Christian missionary to China, Alexander Wylie who wrote:Yi koo yen t'wan...written in 1282 onsists of 64 geometrical problem, illustrated the principle of Plane Measurement, Evolution and other rules, the whole being developed by means of T'een yuen.In 1913 Van Hée translated all 64 problems in Yigu yanduan into French.".
- Yigu_yanduan thumbnail 益古演段.jpg?width=300.
- Yigu_yanduan wikiPageID "25519521".
- Yigu_yanduan wikiPageRevisionID "600143105".
- Yigu_yanduan hasPhotoCollection Yigu_yanduan.
- Yigu_yanduan subject Category:13th-century_works.
- Yigu_yanduan subject Category:Chinese_mathematics.
- Yigu_yanduan comment "Yigu yanduan (益古演段 old mathematics in expanded sections) is a 13th-century mathematical work by Yuan dynasty mathematician Li Zhi. Yigu yanduan was based on North Song mathematician Jiang Zhou (蒋周) Yigu Ji (益古集 Collection of Old Mathematics)which was extinct. However from fragments quoted in Yang Hui's work The Complete Algorithms of Acreage(田亩比类算法大全), we know that this lost mathematical treatise Yigu Ji was about solving area problems with geometry.".
- Yigu_yanduan label "Yigu yanduan".
- Yigu_yanduan label "益古演段".
- Yigu_yanduan sameAs m.0glsqmt.
- Yigu_yanduan sameAs Q8053579.
- Yigu_yanduan sameAs Q8053579.
- Yigu_yanduan wasDerivedFrom Yigu_yanduan?oldid=600143105.
- Yigu_yanduan depiction 益古演段.jpg.
- Yigu_yanduan isPrimaryTopicOf Yigu_yanduan.