Abstract:This paper aims to investigate the geometricproportions, scales, and numerological connotationsembedded within the plans of the capitals of Yuandynasty: Shangdu, Dadu, and Zhongdu. Building uponprevious research, this paper proposes that all threecapitals exhibit distinct geometric proportions in theirlayout plans, primarily manifested in the shape andproportional relationships between the outer city, imperialcity, and palace city within each capital. Additionally,it observes integer multiple relationships between thearea of outer city and palace city (sometimes includingthe imperial city) in each capital. Furthermore, in Daduand Zhongdu, the area of palace cities and rectangularplots occupied by their main halls also displayinteger multiples. Drawing upon ancient architecturalterminologies found in texts such as Zhouli Kaogongji,which describes measurement systems, and YingzaoFashi, which provides architectural principles, thepaper generalized these principles to “inside a capital,everything is measured according to the size of a palace”,“inside a palace everything is measured according to thesize of the main hall”, or “all principles of constructingcapitals are based on the palace.” Moreover, the numericalvalues involved in the aforementioned ratios and scales ofthe three-loop city layout and the main palace (includingblocks, streets, etc.) in each capital, when convertedinto measurement units such as chi, bu, zhang, li, andmu used during Yuan dynasty, carry significant Chinese traditional numerological connotations. These numberssymbolize the ideologies of Yijing (Book of Changes),ancient Chinese astronomy, and the legal calendar,aligning with the knowledge structure and ideologicalsystem attributed to Liu Bingzhong, the main planner ofShangdu and Dadu, who was reputed for his extensiveknowledge in areas such as Yijing and Shao’s JingshiShu, astronomy, geography, the legal calendar, and theThree Methods and Six Ren. This paper sheds light on theprofound connections between the geometric proportions,numerical values, and ideological influences found withinthe layout plans of Yuan’s capitals, providing referencesof the complex intellectual framework and ideologicalsystems of Liu Bingzhong, the principal planner ofShangdu and Dadu.