Two New Approaches for Modeling the Taijitu

Abstract

This article introduces a novel astronomical modeling framework for core concepts in ancient Chinese cosmology. Our work first reconstructed the Taiji typology using numbers from Hetu, this demonstrated that the original Taijitu was likely directly derived from this typology and its numerical configuration, rather than from gnomon shadow-length measurements. This new finding offers a novel perspective on the historical origins of the diagram. Secondly, we showed a real world astronomy perfectly models the Taijitu using a curled solar analemma topology from a dual-hemisphere perspective. This approach effectively solves long-standing modeling challenges, including the non-linear skewing of the central S-curve boundary and the inverted coloration and positioning of the internal eyes at the solstices. Our findings also reveal that the Taijitu is a synthesis of genuine astronomical observations and abstract symbolic transformations used for cultural representation. Third, we identified that the hetu numbers and layout may be derived from the changing rate (dL/dH) of daily sun shadow length and can describe analemma mathematically. Ultimately, these findings bridge the gap between mysterious, abstract cultural symbols and empirical astronomical data.