郭守敬以前八尺圭表在笛卡尔坐标系下的工作机理

The Working Mechanism of Pre-Guo Shoujing 8-chi Gnomon in Cartesian Coordinate System

郭守敬是在继承前人八尺圭表测量的基础之上,对圭表进行的改良。但是《元史·天文志》只是概略描述了郭守敬之前八尺圭表测量的误差特征,而没有揭示背后明确的规律。应用高等数学,研究了郭守敬之前八尺圭表在笛卡尔坐标系下的工作原理,给出了表顶端的投影坐标—本影长度、实影长度、虚影宽度、相对测量精度等4个变量的定义。应用该方法,复现了登封周公测景台台基尺寸,发现郭守敬之前八尺圭表可以在中国中纬度地区进行很好的观测。除本影长度外,称其余3个变量是郭守敬之前八尺圭表的特征信息。这些特征信息是现代科学研究的必要信息,为从新角度研究与郭守敬之前八尺圭表相关的工作,提供了思路。

Guo Shoujing improved the 8-chi gnomon based on inheriting the measurement made by predecessors.However,the Astronomical Records,Yuan Dynasty only briefly describes the error characteristics of pre-Guo Shoujing 8-chi gnomon,without revealing the clear rules behind it.This paper applies advanced mathematics to study the working mechanism of pre-Guo Shoujing gnomon in Cartesian coordinate system,and gives the definitions of four variables of pre-Guo Shoujing 8-chi gnomon,namely the projection coordinates-the length of the umbra,the length of the real image,the width of the imaginary image,and the relative measurement accu racy.Using this method,the size of the base of the Dengfeng Zhougong Observatory was reproduced,and it was found that pre-Guo Shoujing 8-chi gnomons could be well used in the mid-latitude region of China.In addition to the length of the umbra,the remaining three variables are said to be the characteristic information of pre-Guo Shoujing 8-chi gnomon.These characteristic information is for modern scientific research and provide ideas for studying the work related to pre-Guo Shoujing 8-chi gnomon from a new perspective.