Magic SquaresWhat is a Magic Square?
Must consist of a series of numbers arranged in a square such that rows, columns, and diagonals add up to the same amount (the magic total)
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China
Persia
Arabia
India
Europe
Lo Shu Turtle
Magic Charm &
Fortune Telling
Chinese Solar Year
The origin of the magic square is typically linked with Chinese literature  dating back to 650 BC. These legends speak of the  Lo Shu  or "scroll of the river Lo ” where In  ancient China  there was a huge flood and The great king Yu ( ) tried to channel the water out to sea When suddenly a giant turtle emerged with markings on it’s back depicted in the bottom right of this slide.
The dots on the back of this turtle represented the numbers 1-9 and each column, row, and diagonal has the same magic total, in this case 15.
This arrangement of number permeated many facets of the Chinese culture in everything from architecture to fortune telling.
Official buildings were often designed in a 9 square configuration similar to the 9 squares found in the magic square. The number 5 in the center held special significance as this number represented the 5 essential elements in Chinese culture (Metal, wood, fire, water, earth). This number also represented the Emperor or King and thus was majestically placed in the center of the building.
The number 9 is also significant as in many cultures the number 9 often represents “the End” as there is no value greater than nine when using one place value.
The Magic square also gained popularity in magic and fortune telling. If you look at the magic square at the bottom of this slide and draw a line connecting all the numbers in sequential order starting at 1. you are left with a perfectly symmetrical symbol which was often made into necklaces and charms to bring good tidings and fortune to those that carried them.
Lastly, the magic total of this magic square,15, is also the number of days in each of the 24  cycles  of the  Chinese solar year . Adding yet one more layer of significance that the magic square either bolstered or introduced into Chinese culture
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Spread through trade routes
Jabir ibn Hayyan - Father of Islamic Alchemy
The spread of the magic square eastward from China was probably due to the many trade routes in this region.
Upon reaching Islamic and Hindu cultures the magic square maintained the idea of holding special or magical powers.
The magic squares were used in the pseudo science of astrology and again as magic charms with special powers called Yantras
Jabir ibn Hayyan, who is considered the father of Islamic Alchemy, believed that the arrangements of properties could be re-arranged just as the numbers in a magic square can be moved. Hayyan believed that By re-arranging constituent properties of an item one can, through alchemy, completely change the item itself.
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Textile Museum
Pieces from
Sudoku
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The order of the square is 3; that is, the square is a 3x3
The middle value between 1-9 is 5
5x3 = 15
5x3x3 = 15x3 = 45 = 1+2+3+4+5+6+7+8+9
There are many fascinating mathematical truths that we discovered about the magic squares in our research. WE will share just one of these with you here
Take a look at the magic square on this slide. All the number 1 through 9 are represented in this square and the magic total for all the columns, rows and diagonals is 15
This square is essentially a 3x3 grid. In Mathematics we say that The order of the square is 3; This makes sense as there are 9 number in total and 3x3 = 9 so we would need a 3 x 3 grid to house all 9 numbers
The exact middle value between the numbers 1 through 9 is 5
When you multiply 5x3 you get a product of 15 (the magic total) This is a fast way to find out what the magic total for a magic square should be. Find the middle value of the available numbers and multiply it by the order of the square that they would fit into.
Next multiply 5x3x3 This is the same as saying 15x3 and the product of this equation is 45
45 happens to be the total sum of the numbers 1 through 9 added together. Thus, this is a fast way to determine the sum of a series of sequential numbers if you can find the middle value and multiply it by the grid arrangement that these numbers would fall into.
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