The Algorithm and Explanation of the Zhang Heng's Solar Motion
Zhang Heng in the Eastern Han Dynasty annotated the principle and usage of the armillary sphere in his Notes to the Armillary Sphere Diagram.Jia Kui believed that the"solar movement"(solar motion)at a uniform speed on the ecliptic,but the historiographer's measurements of the equatorial degrees show that the solar motion is non-uniform.Zhang Heng believed that transforming the equatorial degrees into the corresponding ecliptic degrees to measure solar motion would bring the solar motion back to its average motion,without any advance or retreat.For this reason,he used thin bamboo strips to appress the surface of the armillary sphere and connect the two poles,measured the corresponding values of the ecliptic and equatorial degrees,and then conducted numerical processing on the measured data.He set up the"identical rate"interval with the same rate of change of the difference between the ecliptic degrees and the equatorial degrees,but different steps in length.He then accumulated the differences between these small intervals to obtain the ecliptic and equatorial degrees on the nodes,and used the linear interpo-lation method to calculate the numerical value between the nodes.Zhang Heng's method is similar to the unequally spaced"spline interpolation"and"numerical integration"methods in modem mathematics,and is a significant in-novation in the history of mathematics both in China and abroad.
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