Sacred Geometry

Lo Shu Square

Also Known As Lo Shu

Form

Citation Formats

General Reference

Divinity Atlas. "Lo Shu Square." Accessed August 30, 2026. https://dev-divinity.interactiveatlas.org/sacred-geometry/lo-shu-square.

APA Style

Divinity Atlas. (n.d.). Lo Shu Square. Retrieved August 30, 2026, from https://dev-divinity.interactiveatlas.org/sacred-geometry/lo-shu-square

BibTeX

@misc{divinityatlas-lo-shu-square,
  author = {Divinity Atlas},
  title = {Lo Shu Square},
  year = {2026},
  url = {https://dev-divinity.interactiveatlas.org/sacred-geometry/lo-shu-square},
  note = {Accessed August 30, 2026}
}

Origin Legend sets the diagram at the flood-tamer Yu, who received it from the Luo River on a turtle's shell; the numbers and their cosmological use are textually secure by the Han dynasty.

The Lo Shu is the three-by-three magic square of Chinese cosmology: the numbers one to nine set so that every row, column and diagonal sums to fifteen, with five at the centre. Legend says it was carried out of the Luo River on the shell of a turtle before the flood-tamer Yu, and the Great Appendix of the Yijing pairs it with the He Tu as one of the two primordial diagrams. As the plan of the Nine Halls it organised the ritual architecture of the imperial mingtang, and it remains the computational ground of feng shui's flying-star schools, making it perhaps the most consequential small diagram in East Asian thought.

Facts

Origins

Origin Period

Legend sets the diagram at the flood-tamer Yu, who received it from the Luo River on a turtle's shell; the numbers and their cosmological use are textually secure by the Han dynasty. 1

Origin Period

The paired dot diagrams of the He Tu and Lo Shu in their familiar form were fixed and canonised in Song dynasty Yijing scholarship. 2

Origin of the Name

Lo Shu, the writing of the Luo River. The Great Appendix of the Yijing pairs it with the He Tu: the Ho gave forth the map, and the Lo the writing. 3

Form

Geometric Form

The unique three-by-three magic square, up to rotation and reflection: 4-9-2 over 3-5-7 over 8-1-6, every row, column and diagonal summing to fifteen, with five at the centre. 1

Category of Sacred Geometry

Form 1

Keyword

Change and Circulation 2

Structure

Odd, yang numbers hold the centre and the cardinal points; even, yin numbers hold the corners. In the traditional diagram each number is a knot of dots, white for odd and black for even, joined by short lines. 1

Attestation

Meaning in the Attesting Source

The square is the plan of the Nine Halls (jiugong): the ritual circuit of the mingtang followed its numbers, and each cell answers to a direction, a season and a trigram in the correlative system. 1Chinese correlative cosmology

Learn More

The Turtle from the Luo

The legend is brief. When the sage-king Yu was taming the great flood, a turtle rose from the waters of the Luo River, and on the plates of its shell were marks: the numbers one to nine, so arranged that every line of three, across, down or corner to corner, sums to fifteen. The Great Appendix of the Yijing names the event in a single breath with its twin: the He gave forth the map, and the Lo gave forth the writing, and the sages took them as pattern. Behind the legend stands a mathematical fact and a long history.

The fact, noted in Schuyler Cammann's classic study, is that the three-by-three magic square is unique: apart from rotations and reflections, there is only one way to arrange one to nine so that every line sums to fifteen, with five inevitably at the centre. The Chinese diagram is therefore not one design among many but the design, discovered rather than invented.

The history is that by the Han dynasty the square was doing serious cosmological work. Its odd, yang numbers hold the centre and the four cardinal points; its even, yin numbers hold the corners; and each cell was correlated with a direction, a season and a trigram of the Yijing. In the traditional figure the numbers are drawn as knots of dots, white for odd and black for even, joined by short bars, the form in which the Song dynasty fixed the diagram and in which it has been printed ever since.

The Nine Halls

The Lo Shu's deepest influence came through architecture and ritual. Read as a floor plan, the square becomes the Nine Halls, jiugong: a building of nine rooms in a three-by-three grid, each room bearing a number and its cluster of correspondences. Han sources describe the mingtang, the cosmic hall of the emperor, in exactly these terms. Moving through the halls in the order of the numbers, the Son of Heaven enacted the circulation of the year, occupying the room that answered to the season and facing the direction whose power was then ascendant, so that the state itself was kept in step with heaven by a walk through a magic square.

Cammann's study traces how the same square organised divination boards, calendrical schemes and the correlative tables through which Chinese thought bound numbers, directions, colours, elements and trigrams into one fabric. The square never retired. The flying-star schools of feng shui still work by moving the nine numbers through the nine palaces in fixed sequences, reading the shifting positions as the fortunes of a building through time, so that a modern practitioner casting a chart is manipulating the Lo Shu as surely as a Han ritualist pacing the mingtang. Nor is the square only Chinese: the same unique order-three arrangement opens the sequence of planetary kameas in Western occult tradition, where it is assigned to Saturn, and this atlas's entries on the kameas begin from the very numbers the turtle carried.

Cross-Tradition Connections