how the ancient scholar form the magic square and what was their techniques
thinkiit pre foundation class viii mental
exactly as the title suggests people
thinkiit prefoundation
squaresDescription complète
A scripture about the abramelin squares.Descripción completa
Description : A scripture about the abramelin squares.
A scripture about the abramelin squares.Full description
bookFull description
Descripción: book
Magic Squares Andrew Yuwen
Types of Magic Squares ● odd vs even ● singly even (6x6 or 10x10) ● doubly even (4x4 or 8x8) ●
History ● Discovered in China, c. 650BCE ● First magic squares (orders 5 and 6) found in Baghdad, Encyclopedia of the Brethren of Purity ● used with “magic letters” in Arabic spirituality, to assist Sufi illusionists
Lo Shu Square ● flooding of the river Lo ● a turtle emerges with a magic square on his shell ● sum was 15, number of days of a cycle in the solar year ● Afterwards, people could predict floods and protect themselves
Lo Shu Square ● unique 3x3 magic square with 1 on bottom and 2 in upper-right corner ● all other 3x3 magic squares are reflections and rotations of this
4
9
2
3
5
7
8
1
6
Chautisa Yantra 7 12 1 14 2 13 8 11 16 3 10 5 9
6 15 4
Chautisa Yantra ● 10th century, Parshvanath Jain temple ● rows, columns, diagonals, 2x2 subsquares, corners of 3x3 and 4x4 squares, middle two entries of outer rows and columns all sum to 34
7 12 1 14 2 13 8 11 16 3 10 5 9
6 15 4
Chautisa Yantra ● every second diagonal number sums to 17 (including short diagonals) ● 8 trapeziums sum to 34 ● 4 triangles with three numbers and a corner sum to 34
7 12 1 14 2 13 8 11 16 3 10 5 9
6 15 4
Melencolia I (Abrecht Durer)
Melencolia I (Abrecht Durer)
Melencolia I (Abrecht Durer) gnomon magic square: sum of quadrants and middle 2x2 square is 34
16 3
2 13
5 10 11 8 9
6
7 12
4 15 14 1
Melencolia I (Abrecht Durer) artist’s name and year
16 3
2 13
5 10 11 8 9
6
7 12
4 15 14 1
Sagrada Familia ● significance of magic constant ● can also be expanded to a magic cube
1 14 14 4 11 7
6
9
8 10 10 5 13 2
3 15
De Occulta Philosophia ● Heinrich Cornelius Agrippa ● magic squares (kameas) represented astrological planets ● highly influential until 16th century counterreformation ● still used in ceremonial magic
Sator Square ● sator - progenitor, originator ● arepo - trust ● tenet - holds, comprehends, preserves ● opera - work, care, aid ● rotas - wheel, rotate ● “The sower works for mastery by turning the wheel.” ● method to overcome envy
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Sator Square and Christianity ● ● ● ● ●
associated with cross of Pater Noster (Our Father, from the Lord’s Prayer) A’s and O’s represent Alpha and Omega way for early Christians to signal each other to avoid persecution the names of the five nails with which Jesus was crucified palindromes could not be tampered with by the devil, who would be confused by the repetition of letters
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Construction of 3x3 Squares ● Edward Lucas ● Every 3x3 magic square is of this form
c-a
c-a-b
c+b
c-a+b
c
c+a-b
c-b
c+a+b
c-a
Construction of Squares ● Magic squares exist for all values of n except 2 ● Odd and doubly even are easy ● Singly even is more difficult
