The square
With North at the bottom and South at the top, as in traditional Chinese diagrams, the Lo Shu reads:
| 4 | 9 | 2 |
| 3 | 5 | 7 |
| 8 | 1 | 6 |
Every row, column and diagonal sums to 15. Odd numbers sit on the cardinal points, even numbers in the corners, and each pair of opposite numbers adds up to 10 (1 + 9, 2 + 8, 3 + 7, 4 + 6) around the 5 in the centre.
Where it comes from
Legend says the pattern appeared as dots on the shell of a turtle that emerged from the Luo River (洛水) in the time of the flood-taming Yu the Great, around 2000 BCE — hence the name, "Luo writing". The square itself is recorded in Chinese texts from the Han dynasty onwards and is one of the oldest known magic squares.
Numbers and directions
| Number | Direction | Trigram | Element |
|---|---|---|---|
| 1 | North | Kan | Water |
| 2 | Southwest | Kun | Earth |
| 3 | East | Zhen | Wood |
| 4 | Southeast | Xun | Wood |
| 5 | Centre | — | Earth |
| 6 | Northwest | Qian | Metal |
| 7 | West | Dui | Metal |
| 8 | Northeast | Gen | Earth |
| 9 | South | Li | Fire |
These are the "home" positions of the numbers, and they're also the Kua numbers' home directions: a Kua 1 person's Fu Wei direction is North, a Kua 9 person's is South.
The flying path
Follow the numbers 5, 6, 7, 8, 9, 1, 2, 3, 4 in the standard square and they trace a fixed route: Centre, Northwest, West, Northeast, South, North, Southwest, East, Southeast. That route is the "flight" of Flying Star feng shui. Put any number in the centre and send it along the route counting up (forward, yang) or down (backward, yin), and you get every possible flying star layout. The annual chart flies forward from the year's number; a natal chart flies its mountain and water stars forward or backward depending on the house's facing.