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	Lo Shu Square - Wikipedia, the free encyclopedia
		The Lo Shu Square, the unique normal magic square of order three that has 1 at the bottom and 2 in the upper right corner, is an important part of Feng Shui, the ancient Chinese art of qi direction with regards to the placement of physical objects and their placement's effect on qi flow.
		A turtle emerged from the water with a curious pattern on its shell, with patterns of circular dots arranged in a three-by-three grid on the shell, such that the sum of the numbers in each row, column and diagonal was the same: 15.
		The Lo Shu square, in the form of a trigram, gives the basis for determining the orientation of buildings, and is also a diagrammatic representation of the seasons showing the ratio of yin and yang in the annual cycle.
	en.wikipedia.org /wiki/Lo_Shu_Square (349 words)

	Magic square - Encyclopedia, History, Geography and Biography
		In mathematics, a magic square of order n is an arrangement of n² numbers in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.
		The earliest magic square of order four was found in an inscription in Khajuraho, India, dating from the eleventh or twelfth century; it is also a panmagic square where, in addition to the rows, columns and main diagonals, the broken diagonals also have the same sum.
		In the magic square of order four, the numbers in the four central squares and one square at each corner are retained in the same place and the others are interchanged with their diametrically opposite numbers.
	www.arikah.net /encyclopedia/Magic_square (1538 words)

	Lo Shu Square - Encyclopedia, History, Geography and Biography
		The Lo Shu Square, the unique normal magic square of order three, is an important part of Feng Shui, the ancient Chinese art of qi direction with regards to the placement of physical objects and their placement's effect on qi flow.
		Then, there emerged from the water a turtle with a curious figure/pattern on its shell; there were circular dots of numbers that were arranged in a three by three nine-grid pattern such that the sum of the numbers in each row, column and diagonal was the same: 15.
		Traditional Chinese cities and temples were laid out in a square broken into nine sections; the odd numbers in the Lo Shu Square are male or yang, while the even numbers are female or yin.
	www.arikah.net /encyclopedia/Lo_Shu_Square (346 words)

	Reference.com/Encyclopedia/Magic square
		In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.
		The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three in which 1 is at the bottom and 2 is in the upper right corner.
		Odd and doubly even magic squares are easy to generate; the construction of singly even magic squares is more difficult but several methods exist, including the LUX method for magic squares (due to John Horton Conway) and the Strachey method for magic squares.
	www.reference.com /browse/wiki/Magic_square (2858 words)

	Magic square Summary
		A magic square is an n x n grid in which numbers have been written in such a way that the sum of the numbers along any row, column, or main diagonal is always the same magic constant.
		The Square of Lo Shu is also referred to as the Magic Square of Saturn or Cronus, which thereby denotes it is the square of time.
		The earliest magic square of order four was found in an inscription in Khajuraho, India, dating from the eleventh or twelfth century; it is also a panmagic square where, in addition to the rows, columns and main diagonals, the broken diagonals also have the same sum.
	www.bookrags.com /Magic_square (2733 words)

	Lo Shu Square
		In the western world, the Lo Shu Square is known as the magic square because the addition of any three numbers in a row total 15.
		The Lo Shu square is placed over the house, room or land where the center is equal to 5.
		Then rotate it until 1 is in the north position, 9 is in the south, 3 in the east and 7 in the west.
	www.angelfire.com /ns/hluong/lss.htm (150 words)

	Encyclopedia: Lo Shu Square
		The unique normal magic square of order 3, also known as the Lo Shu Square.
		Fēng Shuǐ (風水 – literally, wind and water pronounced fung shuway), which may be more than 3000 years old, is the ancient practice of placement to achieve harmony with the environment.
		Yang is the one of the two opposing forces in Chinese philosophy, it associates with the bright Sun, represents masculine nature.
	www.nationmaster.com /encyclopedia/Lo-Shu-Square (903 words)

	Abrahadabra: The Lo Shu #3
		The first actual magical square begins with a 3 x 3 square which appears at row #3 on the Abrahadabra Grid and reveals exactly 9 triangles corresponding to the 9 squares of the Lo Shu, also called the Qamea of Saturn in the Tree of Life.
		This is just a coincidence of geometry in itself but amounts to a compelling argument suggesting that magical squares and their corresponding magical triangle counterparts share some kind of synchronistic relationship that has not been very much observed or explored to the best of my knowledge.
		And yet, in all other respects, magical squares and magical triangles would seem to have little in common, since it is simply not possible to achieve in triangles the exact numerical symmetries found in squares.
	www.abrahadabra.com /LoShu003.htm (771 words)

	Early Heaven (Site not responding. Last check: 2007-10-24)
		With the Lo Shu, the Chinese are acredited with the first known magic square in the history of mathematics.
		There are actually eight different versions of this square, all with the same sum=15 properties, yet the Lo Shu square is identical with the Magical Square of Saturn, a device used in the Western Magical Tradition to denote the powers of the planet/deity Saturn.
		However, there is much confusion regarding the early history of magic squares, and one author has claimed that Neo-Platonists in the 3rd century CE knew the 3 x 3 magic square.
	www.earlyheaven.com /feng_shui/lo_shu.html (508 words)

	hiakZ - Book of Lo (Lo Shu)
		Lo Shu is often drawn in the form of a 9-square chart with each square representing a direction in the compass (see diagram below) namely North, South, East, West, Northeast, Northwest, Southeast, Southwest and the center (total 9 locations).
		The numbers in each square of the Lo Shu embrace a variety of meanings.
		Apart from the 5 in the center, the Lo Shu numbers are arranged such that after every Yang number, a Yin number follows, and, after every Yin number comes a Yang number.
	www.hiakz.com /loshu.asp (303 words)

	AstroVisionOnline.com ->> Lo-Shu Magic Grid
		The Lo Shu Grid or Magic Square is a mysterious pattern that forms the basis for Chinese architectural planning and which symbolizes the natural order of the universe.
		The squares represent the flow of the seasons as well as the rooms of a building or house.
		The trigrams of the Lo Shu Magic Square are arranged in the Later Heaven Sequence which stands for earthly order - as contrasted to the Former Heaven Sequence which expresses heavenly order.
	195.astro.spectrum.in /AVFengShui/loshu-grid.htm (285 words)

	Magic Square
		Unlike the 3x3 square there is not just one conclusion for the distribution of the numbers 1 to 16 in a 4x4 square.
		The Latin square, which is formed by 1,2, and 3 and has different numbers in every row and column, is an example of a semi-magic square.
		A square is panmagic, if it is magic and if the numbers have the same sum in the corners, in the centre and on the edges.
	www.mathematische-basteleien.de /magsquare.htm (919 words)

	Profiles
		Magic squares are tables of numbers arranged in such a way that the rows, columns, and diagonals all add up to the same number.
		Legend has it that magic squares were discovered by the Chinese emperor Yu in 2200 B.C. Yu was reportedly walking along the bank of the Yellow River, and came upon a turtle whose shell was pierced with a series of dots and spots.
		Some, however, believe that magic squares have mystical powers, which is why in some countries magic squares can be found in and on temples, in jewelry and body art, and in pottery and other hand-crafted items.
	www.utica.edu /instadvance/marketingcomm/profiles.cfm?action=detail&id=1 (726 words)

	The Lo Shu
		The Lo Shu is sometimes referred to via a number of different synonyms, for example: The Pagua, The Ba-gua (pronounced Ba-gwa), The Bagua, The Pa Kua.
		The Lo Shu is considered to have it's roots established in the Lo Map and the 9 chamberedsymbology has given rise to different systems of astrology in different cultures:
		In Feng Shui, the Lo Shu is used as anenergetic map and can be overlaid on building layouts and the specific 'gua' (the section of the complete Bagua) traits suchas colour or shape can be used to enhance and harmonize the life of the occupant(s).
	www.fengshui-astrology.com /LoShu.html (770 words)

	Encyclopedia: Timeline of mathematics
		Squaring the circle is the problem proposed by ancient Greek geometers, of using ruler-and-compass constructions, in a finite number of steps, to make a square with the same area as a given circle.
		In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is.
		Least squares is a mathematical optimization technique that attempts to find a best fit to a set of data by attempting to minimize the sum of the squares of the differences (called residuals) between the fitted function and the data.
	www.nationmaster.com /encyclopedia/Timeline-of-mathematics (8072 words)

	Feng Shui New is the biggest and best Feng Shui site on the web , Probably....
		The legendary emperor of China Fu Hsi (xi) is said to have discovered a mythical turtle emerging from the river LO, bearing on it's back an arrangement of numbers from 1 to 9, this arrangement is known as the Lo Shu or the magic square.
		Starting from the centre square (5) moving left (3) = 8 which is the value of the next square in an anticlockwise movement.
		Lets view the Lo Shu from a numerical angle, take all the odd numbers excluding the centre 5, remember we are equating these values to directions so the centre (5) is excluded.
	www.fengshuinew.com /theory.htm (781 words)

	Ã¿: lo shu square
		Lo shu orders the Chinese stages of life 1 through 9 in a square that adds up to 15 in all directions-- diagonally, horizontally and vertically.
		Place the number 3 (for growth) in the wealth spot (the bottom right hand corner of the box - where '6' sits in the lo shu box).
		The symbols are vague enough that the juxtapositions are invariably evocative: Lo shu can function as a kind of random plot generator to test drafts against.
	www.sankey.ca /y/001717.html (410 words)

	ÿ » Blog Archive » lo shu square (Site not responding. Last check: 2007-10-24)
		Lo shu orders the Chinese stages of life 1 through 9 in a square that adds up to 15 in all directions—diagonally, horizontally and vertically.
		Place the number 3 (for growth) in the wealth spot (the bottom right hand corner of the box – where ‘6’ sits in the lo shu box).
		The symbols are vague enough that the juxtapositions are invariably evocative: Lo shu can function as a kind of random plot generator to test drafts against.
	yukaitora.ca /2005/02/02/lo-shu-square (468 words)

	Background of Chinese Feng Shui Purple White Flying Stars
		The Lo Shu square of magic numbers superimposed on the back of a turtle in China thousand years ago.
		Each grid in the Lo Shu square is filled a unique arrangement of the numbers one to nine.
		By combining the Lo Shu square and the Later Heaven Pa Kua symbols (Pa is eight in Chinese), it becomes Nine Palace Eight Kua diagram, which is applied on the areas of Chinese Feng Shui, Medicine, Architecture and Arts.
	www.chineseastrologyonline.com /pwbasic.htm (668 words)

	The History Of Magic Squares (Site not responding. Last check: 2007-10-24)
		The first magic square in history was created in China by an unknown mathematician, sometime before the first century AD.
		“Called the Lo Shu square, it is a magic square of 3 that was said to have appeared on the back of a turtle that came up out of the river.
		Lo Shu supposedly means "river map," and the story of the appearance of the turtle had to do with a sacrifice to the river god” (http://freespace.virgin.net
	www.radessays.com /viewpaper/97271/Malcolm_x.html (209 words)

	9-fold Higher Order Patterning of Tao Te Ching Insights
		The Lo Shu square is associative -- but is not a panmagic square for which all the diagonals --including the broken diagonals obtained by "wrapping around" the edges -- total like the rows and columns.
		The original 3x3 Lo Shu square is far from being bimagic, since the sums of the squared numbers (of the rows or columns) vary between 77 and 107.
		A magic cube is a three-dimensional version of the magic square in which the rows, columns, pillars (or "files"), and four space diagonals each sum to a single number known as the magic constant.
	www.laetusinpraesens.org /docs00s/taote4.php (3509 words)

	Glossary E-F
		Earth is at the center of the eight trigrams in the Lo shu square and Bagua, and represents balance center and grounding.
		Earth-base star: In a flying-star chart, the energy or quality of chi indicated by a number, representing the birth (at the closing of the roof) of a structure, within a proscribed 20-year time cycle, enclosing the earth energies of that time period into the structure.
		Eight-House Feng Shui, also Eight Mansions: Dividing the house into nine sections of the Lo Shu grid determines the four most auspicious and four least auspicious directions and activities for both the person and the building (excluding the center).
	www.intuitiveconcepts.com /glossary_e-f.htm (1256 words)

	AstroVisionOnline.com - Feng Shui : Pa-Kua and Lo-Shu
		After finding out the Kua Number, the next step is Lo Shu numbers which enables to find out the best and worst locations within the Lo Shu grid.
		This pattern came to be known as the Lo Shu.
		The squares in the Lo Shu grid have numbers from 1 to 9.
	195.astro.spectrum.in /AVFengShui/pakua-loshu.htm (234 words)

	Chinese Mathematics: Rebecca And Tommy
		Clearly the Lo Shu is a straight forward magic square in which the integers added up along any column, row or major diagonal add up to 15 (see diagram 9).
		It wasn't until the +13th century that the development of magic squares was introduced into the main current of mathematical thought.
		He recognised that 'if the integers be the consecutive numbers from 1 to n squared, the square is said to be of nth order, and in this case the numbers in any row, column, or diagonal is said to equal (1/2)n(n squared + 1)' (Ball, 1960, p119).
	www.unisanet.unisa.edu.au /07305/magicsq.htm (613 words)

	Pakua Mirror - Sify.com
		The Pakua's potency lies in the arrangement of the Eight Trigrams in the Lo Shu diagram, 5 elements and small mirror in the center.
		8 Trigrams are the numbers which are placed around the lo shu square, which is a 3 x 3 grid.
		Lo shu square is the basis of the fengshui analysis where the numbers are placed in such a way that whether u add them vertically or horizontally, the sum would be 15, like that of the magic square.
	sify.com /astrology/fullstory.php?id=13745813 (355 words)

	The Lo Shu Square : The Legend of the Giant Tortise
		The Lo Shu Square : The Legend of the Giant Tortise
		According to ancient Chinese legends, a giant tortoise surfaced from the River Lo in central China around 4,000 years ago.
		The Lo Shu square became the basic theory of The Flying Star School of Feng Shui.
	web.singnet.com.sg /~cecil/tortise.htm (187 words)

	Amof:Info on Magic Squares
		Notice that all of these squares can be obtained from the first one through flips and turns (rotations) of the first magic square.
		Magic Squares are claimed to go back as far as 2200 BC when the Chinese called them lo-shu.
		The magic squares problem is an example of a problem which is easy to understand, yet hard to solve in general.
	theory.cs.uvic.ca /amof/e_magiI.htm (898 words)

	Welcome To Astrodaily
		It is believed that around 2205 BC, a noble tortoise emerged from the legendary Lo river carrying on its huge back nine numbers that were arranged in a grid pattern.
		The use of the Lo Shu square is widely used in advanced feng shui work.
		One should superimpose the lo shu onto the plan of the house.
	astrodaily.com /fengSui.asp (452 words)

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