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Lo Shu Square


Lo Shu Square (simplified Chinese: 洛书; traditional Chinese: 洛書; pinyin: luò shū; also written 雒書; literally: Luo (River) Book/Scroll), or the Nine Halls Diagram (simplified Chinese: 九宫图; traditional Chinese: 九宮圖; pinyin: jiǔ gōng tú), is the unique normal magic square of order three (every normal magic square of order three is obtained from the Lo Shu by rotation or reflection). Lo Shu is part of the legacy of the most ancient Chinese mathematical and divinatory (Yi Jing 易經) traditions, and is an important emblem in Feng Shui (風水), the art of geomancy concerned with the placement of objects in relation to the flow of qi (氣) "natural energy".

Chinese legends concerning the pre-historic Emperor Yu (夏禹) tell of the Lo Shu, often in connection with the Yellow River Map (Hetu) and 8 trigrams. In ancient China there was a huge deluge: the people offered sacrifices to the god of one of the flooding rivers, the Luo river (洛河), to try to calm his anger. A magical turtle emerged from the water with the curious and decidedly unnatural (for a turtle shell) Lo Shu pattern on its shell: circular dots giving unary (base 1) representations of the integers one through nine are arranged in a three-by-three grid.

Early records are ambiguous, referring to a "river map", and date to 650 BCE, but clearly refer to a magic square by 80 CE, and explicitly give one since 570 CE.


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