Hexagram (Chinese 卦, guà; full name: 六十四卦, liùshísì guà — "the sixty-four symbols") is the main oracular symbol of the I Ching (易經, "Book of Changes", #6), consisting of six lines (爻, yáo): solid (Yang, ⚊) and broken (Yin, ⚋).

Structure of a Hexagram

• Upper trigram (上卦, shàngguà) — Heaven, outer, future
• Lower trigram (下卦, xiàguà) — Earth, inner, past

Read from bottom to top. Lines are numbered from bottom to top (1→6). The first line is the foundation of the situation, the sixth its culmination.

The Complete Combinatorics

64 = 8 × 8. 64 hexagrams = 8 trigrams × 8 trigrams = the complete combinatorics of Yin and Yang over six positions. Each hexagram has a name, an image (象, xiàng), a judgment (彖, tuàn) and texts for individual lines.

Methods of Obtaining a Hexagram

• Traditionally — divination with yarrow stalks (蓍草, shīcǎo, 49 stalks)
• Simplified — three coins (三枚銅錢)

The I Ching and Leibniz

An anticipation of binary code. The binary structure of the hexagrams drew the attention of Leibniz (1703), who saw in it an anticipation of the binary numeral system. This was the first deep encounter between Eastern cosmology and Western mathematics.