Heluo Mathematical Principles, said to be created by Chen Tuan and narrated by Shao Yong (possibly a pseudonymous version), was compiled and edited by Shi Yingxuan during the Chongzhen period of the Ming Dynasty.

Its core method is to use He Tu numbers for earthly branches and Luo Shu numbers for heavenly stems to convert the four pillars of birth (year, month, day, hour) into a six-line hexagram, then analyze the trends presented by the hexagram according to the structure of the I Ching.

From a modern mathematical perspective, this is an ancient application of "remainder theorem + spatiotemporal coding".

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Taking Numbers from Birth Date Pillars

I. Heavenly Stem Numbers (Luo Shu Numbers)

The ancients assigned numbers to the ten heavenly stems based on their trigram attributes, incorporating them into the Later Heaven numbers (Luo Shu) of the eight trigrams.

Mnemonic:

Ren and Jia follow Qian number, Yi and Gui seek Kun. Geng comes to Zhen, Xin stays in Xun. Bing stands at Gen gate, Ji at Li head. Wu must emerge from Kan, Ding is collected in Dui.

Later Heaven trigram numbers:

1 Kan, 2 Kun, 3 Zhen, 4 Xun, 5 Center, 6 Qian, 7 Dui, 8 Gen, 9 Li

Table:

II. Earthly Branch Numbers (He Tu Numbers)

Mnemonic:

Hai and Zi are 1 and 6 water Yin and Mao are 3 and 8 true Si and Wu are 2 and 7 fire Shen and You are 4 and 9 metal Chen, Xu, Chou, Wei are 5 and 10 earth

Table:

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III. Example of Taking Numbers from Stems and Branches

Take 2025-11-20 18:10 (male) as an example: Four pillars: Yi Si, Ding Hai, Gui Si, Xin You

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IV. Numerical Operations (Heaven Number, Earth Number)

Heaven and Earth Base Numbers

From He Tu Heaven and Earth numbers:

• Total Heaven Number: 25
• Total Earth Number: 30

① Sum of odd numbers as Heaven Number

In the example, heavenly stem numbers are: 2, 7, 2, 4

Add the odd parts of earthly branches (e.g., 7, 1, 7, 9)

Sum all odd numbers → get Heaven Number.

② Sum of even numbers as Earth Number

Sum all even numbers → get Earth Number.

③ Derive trigram from Heaven Number (mod 25 operation)

If equal to 25 → take 5 If less than 25 → take the units digit If greater than 25 → divide by 25 and take the units digit of the remainder

Example:

7+7+1+7+9=31/25 remainder 6

④ Derive trigram from Earth Number (mod 30 operation)

Look at the Earth Number obtained, method same as Heaven Number but base is 30. If exactly 30, use 3. If less than 30, also take the units digit; if greater than 30, divide by 30 and take the units digit of the remainder. Example: 2+2+4+2+6+2+4=22, take 2

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V. Derive the Innate Trigram (Form Hexagram Based on Remainder)

If remainder is 5, need to determine the lodestar based on birth cosmic period (lower period lodges in Li/Dui).

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VI. Three Cosmic Periods Lodestar (Used When Remainder is 5)

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VII. Trigrams Interacting to Form Hexagram (Yin-Yang Fate Arrangement)

Trigrams form a hexagram through the interaction of Heaven Number and Earth Number.

Yin-Yang fate determination:

• Yang fate: Zi, Yin, Chen, Wu, Shen, Xu
• Yin fate: Chou, Mao, Si, Wei, You, Hai

Arrangement:

• Yang male / Yin female → Heaven above, Earth below
• Yin male / Yang female → Earth above, Heaven below

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VIII. Final Hexagram Formation in Example

In the example, year pillar is Si → Yin fate

Male → Yin male

Therefore:

• Earth Number (2) above → Kun

• Heaven Number (6) below → Qian

Formed hexagram:

Earth over Heaven: Tai (Peace)

Image meaning: Upper and lower in harmony, qi flows smoothly, structure shows stable and smooth signs.

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Next article will discuss: How to further calculate the moving line (Yuantang number) and the Acquired Hexagram based on Heaven Number and Earth Number?