魏晋南北朝时期穹隆顶墓室结构与牟合方盖

Tomb Structure and Steinmetz Solid in Western Jin Dynasty:A Preliminary Study of Tomb Typology

在东汉到南北朝时期的考古发掘中,大量墓室的穹隆顶,都采用了一种特殊的数学模型:牟合方盖。这个数学模型,是魏晋时期的数学家刘徽构造的。由于牟合方盖本身具备天圆地方的几何特征,因此,墓室穹隆顶的牟合方盖结构的发现与认证,对中国古代的墓葬建筑文化的研究具有重要的价值。从墓葬类型学的角度,根据郑州上街西晋墓室结构的讨论,初步构建了东汉到南北朝时期采用牟合方盖为穹隆顶结构的墓室的标准模型。

The ancient tomb is the most common underground structure in archaeological excavation and the structure of the tomb enjoys important research value in architectural aesthetics,mathematical model and astronomical significance.In recent years of archaeological practice,it can be frequently seen that a large number of tombs from the Eastern Han dynasty to the Southern and Northern dynasties adopted a special dome structure with a square cross section.The longitudinal section of the middle point of all the square sides across the dome forms a semicircle,and the whole dome of the tomb resembles a very important mathematical model-Steinmetz solid,built by Liu Hui,a mathematician in the Wei-Jin period.This model is a geometry of special shape built by Liu Hui for the purpose of deducing the volume of a sphere and proving it,which is widely applied in reality.However,the fact that this model appears in the structure of ancient Chinese tomb architecture seems to have gone unnoticed by researchers in the field of the history of science,archaeology and history.From the perspective of tomb typology,this paper briefly discusses the structure of Western Jin dynasty tombs in Shangjie district of Zhengzhou.By cleaning the measured data of the four tombs M2 and M3,the design model of western Jin dynasty tombs in Shangjie district of Zhengzhou was rebuilt.It was found that the bottom height of each tomb,no matter how high,was 184 centimeters;and the vault is half circular in profile and half as high as the bottom of the tomb.Therefore,a standard model of the tombs with the domed structure adopting Steinmetz solid from the Eastern Han dynasty to the Southern and Northern dynasties is preliminarily constructed.If the height of the bottom is set as 184 centimeters,the length of the sides of the tombs is the only parameter to determine the size of the tombs.In addition,this paper also examines some newly discovered tombs with the domed structure adopting Steinmetz solid from the Eastern Han dynasty to the Southern and Northern dynasties,and finds that not all of the tombs of this structure chose 184cm as the bottom height.The geometric characteristics of the Steinmetz solid can perfectly reflect the model of the hemispherical dome cosmology.The introduction of such a mathematical structure into the design model of the tomb architecture conforms to the desire of the ancients to communicate with heaven and earth.It is the first time that it has been certified in the ancient Chinese tomb architecture as the real object model adopting Steinmetz solid,which is of great value to the study of the ancient Chinese tomb architecture culture.The appearance of the tomb structure is close to the life of Liu Hui in Wei-Jin period,so the relationship between the two is worth further study.At the same time,we can expect that through more new archaeological excavations,the mathematical model of the tomb structure of the Western Jin dynasty will be standardized from the perspective of typology,so as to establish a simple,referable,and highly explanatory sequence parameter and mathematical model for tomb archaeology.