Fitting Taiyi Accumulated Numbers to the Three-Yuan Nine-Period and Two-Yuan Eight-Period Calculations

According to Wang Ximing's "Taiyi Golden Mirror Formula," as recorded: in the Jia-Zi year of the twelfth year of Kaiyuan, the upper yuan's accumulated years amount to 1,937,281 counts. This places CE 724 at 1,937,281 counts; because antiquity had no zero count, 1 count is taken as Jia-Zi. If one wishes to correct by the sequential ordinal of Jia-Zi, the upper yuan accumulated years for CE 724 become 1,937,280, and CE year 0 is 1,936,556 counts. The Three-Yuan Nine-Period and Two-Yuan Eight-Period are both derived from this. For example, the Three-Yuan Nine-Period year 2004: 1,936,556 + 2004, divide by 20, then take modulo 9, yielding the eighth period—identical to the present Three-Yuan Nine-Period calculation. Also, 180 years is precisely the cycle of three yuan or two yuan, so the Two-Yuan Eight-Period must likewise correspond. Thus one may know that both the Three-Yuan Nine-Period and the Two-Yuan Eight-Period ultimately derive from the Taiyi accumulated numbers.