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PYTHAGORAS TETRAKTYS
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PYTHAGORAS TETRAKTYS
ROWS OF THE TETRAKTYS = MAGIC SQUARE CONSTANTS
1
2+3
4+5+6 =15 = Magic Square of 3x3 (M.Sq. 3)
7+8+9+10 = 34 = (M.Sq. 4)
11+12+13+14+15 = 65 = (M.Sq. 5)
16+17+18+19+20+21 = 111 = (M.Sq. 6)
22+23+24+25+26+27+28 = 175 = (M.Sq. 7)
29+30+31+32+33+34+35+36 = 260 = (M.Sq. 8)
37+38+39+40+41+42+43+44+45 = 369 = (M.Sq. 9)
46+47+48+49+50+51+52+53+54+55 = 505 = (M.Sq. 10)
Observe that the last digits on the right hand side: 1-3-6-10-15-21-28- etc form the Sequence of Triangular Numbers being, 1, 1+2=3, 1+2+3=6, 1+2+3+4=10, 1+2+3+4+5=15, 1+2+3+4+5+6=21 etc.
The Natural Square of 3x3 already has its 2 diagonals summing to 15.
This Magic Square of 3x3 has 3 vertical sums of 15, 3 horizontal rows of 15 and 2 diagonals of 15. Thus the Magic Square Sum or Constant is 15.
This ancient Pythagorean Triangle of 10 Dots in a Triangle was believed to contain the formation of the 5 Platonic Solids.
“The Pythagorean Tetraktys, revered by Platonists, was the square placed below the triangle; the latter or Trinity, embodying the invisible Monad - the Unity, and deemed too sacred to be pronounced except within the walls of a Sanctuary”. (-H.P. Blavatsky, Isis Unveiled, 11, 419)
The Tetraktys has its roots in an ancient Puzzle: Can you make this House using 8 lines, and without lifting your pencil from the paper? The Germans have an expression with 8 syllables: recited as they draw each line: “Das ist das Haus vom Ni-ko-laus”
“I remember as a 7 year old child, being thrilled that I could draw this House with 8 lines, unicursally, returning to the place that I started from”.
Jain 108
ROWS OF THE TETRAKTYS = MAGIC SQUARE CONSTANTS
1
2+3
4+5+6 =15 = Magic Square of 3x3 (M.Sq. 3)
7+8+9+10 = 34 = (M.Sq. 4)
11+12+13+14+15 = 65 = (M.Sq. 5)
16+17+18+19+20+21 = 111 = (M.Sq. 6)
22+23+24+25+26+27+28 = 175 = (M.Sq. 7)
29+30+31+32+33+34+35+36 = 260 = (M.Sq. 8)
37+38+39+40+41+42+43+44+45 = 369 = (M.Sq. 9)
46+47+48+49+50+51+52+53+54+55 = 505 = (M.Sq. 10)
Observe that the last digits on the right hand side: 1-3-6-10-15-21-28- etc form the Sequence of Triangular Numbers being, 1, 1+2=3, 1+2+3=6, 1+2+3+4=10, 1+2+3+4+5=15, 1+2+3+4+5+6=21 etc.
The Natural Square of 3x3 already has its 2 diagonals summing to 15.
This Magic Square of 3x3 has 3 vertical sums of 15, 3 horizontal rows of 15 and 2 diagonals of 15. Thus the Magic Square Sum or Constant is 15.
This ancient Pythagorean Triangle of 10 Dots in a Triangle was believed to contain the formation of the 5 Platonic Solids.
“The Pythagorean Tetraktys, revered by Platonists, was the square placed below the triangle; the latter or Trinity, embodying the invisible Monad - the Unity, and deemed too sacred to be pronounced except within the walls of a Sanctuary”. (-H.P. Blavatsky, Isis Unveiled, 11, 419)
The Tetraktys has its roots in an ancient Puzzle: Can you make this House using 8 lines, and without lifting your pencil from the paper? The Germans have an expression with 8 syllables: recited as they draw each line: “Das ist das Haus vom Ni-ko-laus”
“I remember as a 7 year old child, being thrilled that I could draw this House with 8 lines, unicursally, returning to the place that I started from”.
Jain 108
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