Summary
In the traditional calendars of Mainland Southeast Asia (except for Vietnam), the sidereal year is usually used instead of the tropical year. Since these calendars are lunisolar calendars, a certain cycle of intercalation is needed, and the 19-year cycle is usually used. This cycle is harmonious with a tropical year, but is not with a sidereal year. This fact obliges us to suspect that the origins of the sidereal year and that of the 19-year cycle are different. There is almost no room to doubt the Indian origin of the sidereal year. However, the origin of the 19-year cycle is controversial. It is supposed that the Tai people in South China received the influence of the Chinese calendar. I suspect that the “modified Taichu calendar” (Eastern Han Dynasty) might have been the origin of the 19-year and 57-year cycles used in the Tai calendar and other Mainland Southeast Asian calendars.
Yukio Ôhashi obtained a Ph.D. in the history of mathematics from Lucknow University under the guidance of Prof. K. S. Shukla, and also completed his doctorate course at Hitotsubashi University (Japan) in the social history of the East.
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Ôhashi, Y. (2009). Mainland Southeast Asia as a Crossroads of Chinese Astronomy and Indian Astronomy. In: Yadav, B., Mohan, M. (eds) Ancient Indian Leaps into Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4695-0_13
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