Lo Shu Square, or the Nine Halls Diagram, is the unique normal magic square of order three. The Lo Shu is part of the legacy of ancient Chinese mathematical and divinatory traditions, and is an important emblem in Feng Shui, the art of geomancy concerned with the placement of objects in relation to the flow of qi "natural energy".
History
A Chinese legend concerning the pre-historic Emperor Yu tell of the Lo Shu, often in connection with the Yellow River Map 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, to try to calm his anger. A magical turtle emerged from the water with the curiously unnatural Lo Shu pattern on its shell: circular dots representing the integers 1 through 9 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. Recent publications have provided support that the Lo Shu Magic Square was an important model for time and space and served as a basis for city planning, tomb design, and temple design. The Magic Square was used to designate spaces of political and religious importance. and the Eight trigrams, all carried by a large turtle. This example drawn by an anonymous Tibetan artist. The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15. Since 5 is in the center cell, the sum of any two other cells that are directly through the 5 from each other is 10. The Lo Shu is sometimes connected numerologically with the Bagua, which can be arranged in the 8 outer cells, reminiscent of circular trigram diagrams. Because north is placed at the bottom of maps in China, the 3x3 magic square having number 1 at the bottom and 9 at the top is used in preference to the other rotations/reflections. As seen in the "Later Heaven" arrangement, 1 and 9 correspond with ☵ Kǎn 坎 "Water 水" and ☲ Lí 離 "Fire 火" respectively. In the "Early Heaven" arrangement, they would correspond with ☷ Kūn 坤 "Earth 地" and ☰ Qián 乾 "Heaven 天" respectively. Like the Yellow River Map, the Lo Shu square, in conjunction with the 8 trigrams, is sometimes used as a mandalic representation important in Feng Shui geomancy.
