The magic square方塊數字排列魔術
Transcript of The magic square方塊數字排列魔術
Albrecht Dürer
And his Magic Square
Albrecht Dürer (1471-1528)is considered to be a famous German artist
In 1514 he produced and engaving entitled "melancolie“ in which his Magic Square, the first in Europe, was shown.
The title of this work was intending to show the 4 temperamental elements named "sanguine", "choleric", "melancholic" and "phlegmatic" after the bodily humors).
Each was the result of an excess of one of the humors that produced, in turn, the imbalance in paired qualities
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In his engraving “Melancolie”,
Albrecht Dürer placed his
arithmetical magic square.
You can see it on the right side of
the wall.
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Close up of panel.
But what is magicalAbout it ?
The Number 34 !
This is the sum of the numbers of each field on
the square.
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
The sum of each horizontal line is 34 !
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Each column totals 34 !
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
The 4 corners add up to 34 !
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
If you select the squares (leaving 2 blanks between the each square) in a clockwise direction the total is still 34!
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Try it again in the same manner and it‘s always 34
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
The central squares add up to 34 !
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
And these, 34 !
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
As well as the diagonals . . .
GREAT !
Dürer was very proud to have created the square.
¡¡¡Well there was no televison then !
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Carry on like this: 34 !
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Lastly, the two middle centre at the base of
the square give the date the square was
invented (1514).