At a glance
- Luoshu sums
- Each row, column and diagonal totals fifteen
- Center
- Five in Luoshu
Definition and terminology
The Xici refers to a diagram from the Yellow River and a writing from the Luo River. Later traditions associate them with culture heroes. Familiar Hetu diagrams group numbers one through ten; Luoshu arranges one through nine. Narrative, textual reference and fully developed diagram must be distinguished as historical evidence.
Structure and rules
The usual Hetu pairs are 1/6, 2/7, 3/8, 4/9 and 5/10, associated respectively with water, fire, wood, metal and earth. Luoshu places five centrally and forms a magic square with line sums of fifteen. With south at top, its rows are 4-9-2, 3-5-7 and 8-1-6.
Worked reading
A learner can add 4+9+2 and 4+5+6, obtaining fifteen in both cases. Rotating the paper changes which row appears at the top, while the arithmetic property remains. That checkable property differs from traditional claims that river diagrams reveal cosmic order; the latter belong to the history of ideas.
Context and limits
River diagrams became prominent in Song-period Changes interpretation, but their origins and identifications were disputed. The Siku account of Dunjia Yanyi criticizes equating early Luoshu references with later dot diagrams. Subsequent systems reuse these numbers differently. An illustration should state its orientation, version and correspondence scheme.
References & further reading
Historical sources document ideas and rules of their time, not empirical proof of predictive accuracy. Source notes identify the nature and scope of each reference.
- 《易传·系辞上》Primary / tradition source
Public-domain commentary; traditional accounts of polarity, taiji, images and stalk divination; traditional attribution is not settled authorship.
- 《遁甲演义》（四库全书本）Primary / tradition source
Public-domain Qimen source; editorial account distinguishes legends from documentation and describes palaces, stems, doors and stars.