• Journal for History of Mathematics
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• v.29 no.6
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• pp.325-333
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• 2016

Chinese Mathematics during the period of Jin (1115-1234) and Yuan (1271-1368) is an integral part of the high achievements of traditional mathematics during the Song (962-1279) and Yuan dynasties, which is another peak in the history of Chinese mathematics, following the footsteps of the high accomplishments during the Warring States period (475-221 BCE), the Western Han (206 BCE-24 ADE), Three Kingdoms (220-280 AD), Jin dynasty (265-420 AD), and Southern and Northern Dynasties (420-589 AD). During the Jin-Yuan period, Quanzhen Taoism was a dominating branch in Taoism. It offered certain political protection and religious comforts to many during troubled times; it also provided a relatively stable environment for intellectual development. Li Ye (1192-1279), Zhu Shijie (fl. late 13th C to early 14th C) and Zhao Youqin (fl. late 13th C to early 14th C), the major actors and contributors to the Jin-Yuan Mathematics achievements, were either heavily influenced by the philosophy of Quanzhen Taoism, or being its followers. In certain Taoist Classics, Li Ye read the records of the relations of a circle and nine right triangles which has been known as Dongyuan jiurong 洞渊九容 of Quanzhen Taoism. These relations made significant contributions in the study of the circles inscribed in a right triangle, the reasoning of which directly led to the birth of the Method of Celestial Elements (Tianyuan shu 天元术), which further developed into the Method of Two Elements (Eryuan shu ⼆元术), the Method of Three Elements (Sanyuan shu 三元术) and the Method of Four Elements (Siyuan shu 四元术).

• Journal of the Korean Institute of Landscape Architecture
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• v.37 no.6
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• pp.85-95
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• 2010

East-Asian intellectual societies in the pre-modem age sustained a holistic system of poem-calligraphy-painting trinity until the coming of Western modernism. Therefore, it has been insisted that the principles of traditional landscape gardening were greatly influenced by those of landscape painting and related literature. This study examined those influences closely to discover the essence of traditional Asian landscape architecture through a comparative study between Chinese landscape painting theory and landscape gardening theory within the dual categories of 'contents(value and meaning)' and 'form(view and spatial structure)'. The most important theme of landscape painting theory in contents category was 'Chi and its Vitality(氣韻生動)'. The matching theme in landscape design field was 'Feng-Shui(風水)' and 'Yi-Jin'g(意境)'. The most important theme of landscape painting theory in formal category was 'the Three Ru1es of Perspective(三遠法)'. And the matching theme of landscape design theory was 'Yindi(因地)' and 'Jie-Jing(借景)'. The most important theme of landscape painting theory in formal category was 'the Three Rules of Perspective(三遠法)'. And the matching theme of landscape design theory was 'Yindi(因地)' and 'Jie-Jing(借景)'. It was found that themes and various principles of both fields were closely inter-related and have much in common in their representation of contents and form. In the close relationship with main art genres like this, the landscape gardening could have been recognized as one of the genres of fine art.