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__NOTOC__ Lo Shu Square (; also written ; literally: Luo (River) Book/Scroll), or the Nine Halls Diagram (), is the unique normal
magic square rotation and reflection) non-trivial case of a magic square, order 3 In recreational mathematics Recreational mathematics is mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), ...

magic square
of order three (every normal magic square of order three is obtained from the Lo Shu by rotation or reflection). The Lo Shu is part of the legacy of ancient Chinese mathematical and divinatory (cf. the
I Ching The ''I Ching'' or ''Yi Jing'' (, ), usually translated as ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination Divination (from Latin ''divinare'', 'to foresee, to foretell, to predict, to prophesy') is the at ...
) traditions, and is an important emblem in ''
Feng Shui Feng shui, also known as Chinese geomancy Geomancy (Greek language, Greek: γεωμαντεία, "earth divination") is a method of divination that interprets markings on the ground or the patterns formed by tossed handfuls of soil, ro ...

Feng Shui
'' (), the art of geomancy concerned with the placement of objects in relation to the flow of
qi
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 The Yellow River Map, Scheme, or Diagram (, with variants for the second character) is an ancient Chinese concept. It is related to the Lo Shu Square. The origins of the two from the rivers Luo and Yellow River, He are part of Chinese mythology. ...
(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 (), to try to calm his anger. A magical
turtle Turtles are an of s known as Testudines, characterized by a developed mainly from their ribs. Modern turtles are divided into two major groups, the s and which differ in the way the head retracts. There are 360 living and recently extinct ...

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. 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 (outnumbering the even numbers by one) 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 (the number of days in each of the 24 cycles of the Chinese solar year). 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 (e.g., opposite corners add up to 10, the number of the
Yellow River Map The Yellow River Map, Scheme, or Diagram (, with variants for the second character) is an ancient Chinese concept. It is related to the Lo Shu Square. The origins of the two from the rivers Luo and Yellow River, He are part of Chinese mythology. ...
(). The Lo Shu is sometimes connected numerologically with the
Bagua The Bagua, Pakua or Palgwae are eight symbols used in to represent the fundamental principles of reality, seen as a range of eight interrelated concepts. Each consists of three lines, each line either "broken" or "unbroken", respectively re ...

Bagua
( "8 trigrams"), 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 rotation and reflection) non-trivial case of a magic square, order 3 In recreational mathematics Recreational mathematics is mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), ...

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 "Water " and ☲ Lí "Fire " respectively. In the "Early Heaven" arrangement, they would correspond with ☷ Kūn "Earth " and ☰ Qián "Heaven " respectively. Like the
Yellow River Map The Yellow River Map, Scheme, or Diagram (, with variants for the second character) is an ancient Chinese concept. It is related to the Lo Shu Square. The origins of the two from the rivers Luo and Yellow River, He are part of Chinese mythology. ...
(), the Lo Shu square, in conjunction with the 8 trigrams, is sometimes used as a
mandalic
mandalic
representation important in
Feng Shui Feng shui, also known as Chinese geomancy Geomancy (Greek language, Greek: γεωμαντεία, "earth divination") is a method of divination that interprets markings on the ground or the patterns formed by tossed handfuls of soil, ro ...

Feng Shui
()
geomancy Geomancy (Greek language, Greek: γεωμαντεία, "earth divination") is a method of divination that interprets markings on the ground or the patterns formed by tossed handfuls of soil, rocks, or sand. The most prevalent form of divinator ...
.


See also

* Associative magic square *
Sator Square The Sator Square (or Rotas Square) is a two-dimensional word square containing a five-word Latin palindrome. It features in early Christian as well as in magical contexts. The earliest example of the square dates from the ruins of Pompeii ...
*
Tetractys The tetractys ( el, τετρακτύς), or tetrad, or the tetractys of the decad is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the f ...

Tetractys
*
Yellow River Map The Yellow River Map, Scheme, or Diagram (, with variants for the second character) is an ancient Chinese concept. It is related to the Lo Shu Square. The origins of the two from the rivers Luo and Yellow River, He are part of Chinese mythology. ...
* Camunian rose


Notes


References

* * *


Further reading

* *


External links

*{{commons category inline, Luoshu
Lo Shu Square: Definition, Nature and History
Chinese folk religion
Numerology {{Cat main, Numerology Divination Numbers Mathematics and mysticism Symbolism Pseudomathematics ...
Magic squares Geomancy Divination zh:河圖洛書