T H E G O D S A N D B O O K O F D E A D A N C I E N T E G Y P T A N D B O O K O F L I V I N G M O D E R N T O R U S
 

-=^=-

GoD
 




G O L D E N    S P I R A L

Approximate logarithmic spirals can occur in nature, for example the arms of spiral galaxies - golden spirals are one special case of these logarithmic spirals, although there is no evidence that there is any general tendency towards this case appearing. Phyllotaxis is connected with the golden ratio because it involves successive leaves or petals being separated by the golden angle; it also results in the emergence of spirals, although again none of them are (necessarily) golden spirals. It is sometimes stated that spiral galaxies and nautilus shells get wider in the pattern of a golden spiral, and hence are related to both φ and the Fibonacci series. In truth, spiral galaxies and nautilus shells (and many mollusk shells) exhibit logarithmic spiral growth, but at a variety of angles usually distinctly different from that of the golden spiral. This pattern allows the organism to grow without changing shape.

Platonic solid


FIRE

AIR

WATER

EARTH

AETHER
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

It is constructed by congruent (identical in shape and size),
regular (all angles equal and all sides equal),
polygonal faces with the same number of faces meeting at each vertex.

Five solids meet these criteria.





3


6


9


60

3*60=180



60

3*60=180





60*2=120
60*3=180
60*4=240
60*5=300
60*6=360
60*7=420
60*8=480
60*9=540

60

3*60=180

180*2=360
180*3=540
180*4=720
180*5=900
180*6=1080
180*7=1260
180*8=1440
180*9=1620
180*10=1800
180*11=1980
180*12=2160

90*2=180
90*3=270
90*4=360
90*5=450
90*6=540
90*7=630
90*8=720
90*9=810

90

4*90=360

360*2=720
360*3=1080
360*4=1440
360*5=1800
360*6=2160
360*7=2520
360*8=2880
360*9=3240

108*2=216
108*3=324
108*4=432
108*5=540
108*6=648
108*7=756
108*8=864
108*9=972

108

5*108=540

540*2=1080
540*3=1620
540*4=2160
540*5=2700
540*6=3240
540*7=3780
540*8=4320
540*9=4860

120*2=240
120*3=360
120*4=480
120*5=600
120*6=720
120*7=840
120*8=960
120*9=1080

120

6*120=720

720*2=1440
720*3=2160
720*4=2880
720*5=3600
720*6=4320
720*7=5040
720*8=5760
720*9=6480


128,571

7*128,571=899,99


135*2=270
135*3=405
135*4=540
135*5=675
135*6=810
135*7=945
135*8=1080
135*9=1215

135

8*135=1080

1080*2=2160
1080*3=3240
1080*4=4320
1080*5=5400
1080*6=6480
1080*7=7560
1080*8=8640
1080*9=9720

140*2=280
140*3=420
140*4=560
140*5=700
140*6=840
140*7=980
140*8=1120
140*9=1260

140

9*140=1260

1260*2=2520
1260*3=3780
1260*4=5040
1260*5=6300
1260*6=7560
1260*7=8820
1260*8=10080
1260*9=11340


Tetrahedron
Vertex
3.3.3

FIRE

4 FACES
4 POINTS
6 EDGES

180*4=720


Octahedron
Vertex
3.3.3.3

AIR

8 FACES
6 POINTS
12 EDGES

180*8=1440


Icosahedron
Vertex
3.3.3.3.3

WATER

20 FACES
12 POINTS
30 EDGES

180*20=3600


Hexahedron
Vertex
4.4.4

EARTH

6 FACES
8 POINTS
12 EDGES

360*6=2160


Dodecahedron
Vertex
5.5.5

AETHER

12 FACES
20 POINTS
30 EDGES

540*12=6480





D U A L    P O L Y H E D R A






P E R F E C T    N U M B E R

In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.
For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number.


The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum.

For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 * 28.

Euclid proved that 2p-1(2p-1) is an even perfect number whenever 2p-1 is prime.
For example, the first four perfect numbers are generated by the formula 2p-1(2p-1), with p a prime number, as follows:

for p = 2: 21(22 - 1) = 2 * 3 = 6
for p = 3: 22(23 - 1) = 4 * 7 = 28
for p = 5: 24(25 - 1) = 16 * 31 = 496
for p = 7: 26(27 - 1) = 64 * 127 = 8128

Owing to their form, 2p-1(2p - 1), every even perfect number is represented in binary form as p ones followed by p - 1 zeros.
For example,

610 = 22 + 21 = 1102
2810 = 24 + 23 + 22 = 111002
49610 = 28 + 27 + 26 + 25 + 24 = 1111100002
812810 = 212 + 211 + 210 + 29 + 28 + 27 + 26 = 11111110000002




42
/   \
2     21
/       /   \
2      3      7


42
/   \
6      7
/   \      \
2      3      7
  n=2   =>   x = 13 + 33 = 28
n=3   =>   x = 13 + 33 + 53 = 153
n=4   =>   x = 13 + 33 + 53 + 73 = 496
n=5   =>   x = 13 + 33 + 53 + 73 + 93 = 1225
n=6   =>   x = 13 + 33 + 53 + 73 + 93 + 113 = 2556
n=7   =>   x = 13 + 33 + 53 + 73 + 93 + 113 + 133 = 4753
n=8   =>   x = 13 + 33 + 53 + 73 + 93 + 113 + 133 + 153 = 8128

n=64   =>   x = 13 + 33 + 53 + 73 + 93 + 113 + 133 + 153 + ... + = 33 550 336






3D MIRROR IN MATH

Shouts of FITO technology.

POSITIVE SPHERA   |   NEGATIVE SPHERA

maximum Positive : 6 * 2 = 12 | maximum Negative : 6 * 2 = 12

   1,1,2,3,5,8,4,3,7,1,8,9,   |   8,8,7,6,4,1,5,6,2,8,1,9,..
12   |   21
12 * 2 = 24   |   21 * 2 = 42
4 + 4 + 4 + 12 = 24   |   42 = 6 * 7                

BOW



1,1,2,3,5,8,4,3,7,1,8,9,   8,8,7,6,4,1,5,6,2,8,1,9,..
1+1+2+3+5+8+4+3+7+1+8+9+8+8+7+6+4+1+5+6+2+8+1+9=117 => 1+1+7=9


BEGIN IN G
12   |   21


1
1
2
3
5
8
13 => 1+3=4
21 => 2+1=3
34 => 3+4=7
55 => 5+5=10 => 1+0=1
89 => 8+9=17 => 1+7=8
144 => 1+4+4=9

233 => 2+3+3=8
377 => 3+7+7=17 => 1+7=8
610 => 6+1+0=7
987 => 9+8+7=24 => 2+4=6
1597 => 1+5+9+7=22 => 2+2=4
2584 => 2+5+8+4=19 => 1+9=10 => 1+0=1
4181 => 4+1+8+1=14 => 1+4=5
6765 => 6+7+6+5=24 => 2+4=6
10946 => 1+0+9+4+6=20 => 2+0=2
17711 => 1+7+7+1+1=17 => 1+7=8
28657 => 2+8+6+5+7=28 => 2+8=10 => 1+0=1
46368 => 4+6+3+6+8=27 => 2+7=9

75025 => 7+5+0+2+5=19 => 1+9=10 => 1+0=1
121393 => 1+2+1+3+9+3=19 => 1+9=10 => 1+0=1
196418 => 1+9+6+4+1+8=29 => 2+9=11 => 1+1=2
317811 => 3+1+7+8+1+1=21 => 2+1=3
514229 => 5+1+4+2+2+9=23 => 2+3=5
832040 => 8+3+2+0+4+0=17 => 1+7=8
1346269 => 1+3+4+6+2+6+9=31 => 3+1=4
2178309 => 2+1+7+8+3+0+9=30 => 3+0=3
3524578 => 3+5+2+4+5+7+8=34 => 3+4=7
5702887 => 5+7+0+2+8+8+7=37 => 3+7=10 => 1+0=1
9227465 => 9+2+2+7+4+6+5=35 => 3+5=8
14930352 => 1+4+9+3+0+3+5+2=27 => 2+7=9

24157817 => 2+4+1+5+7+8+1+7=35 => 3+5=8
39088169 => 3+9+0+8+8+1+6+9=44 => 4+4=8
63245986 => 6+3+2+4+5+9+8+6=43 => 4+3=7
102334155 => 1+0+2+3+3+4+1+5+5=24 => 2+4=6
165580141 => 1+6+5+5+8+0+1+4+1=31 => 3+1=4
267914296 => 2+6+7+9+1+4+2+9+6=46 => 4+6=10 => 1+0=1
433494437 => 4+3+3+4+9+4+4+3+7=41 => 4+1=5
701408733 => 7+0+1+4+0+8+7+3+3=33 => 3+3=6
1134903170 => 1+1+3+4+9+0+3+1+7+0=29 => 2+9=11 => 1+1=2
1836311903 => 1+8+3+6+3+1+1+9+0+3=35 => 3+5=8
2971215073 => 2+9+7+1+2+1+5+0+7+3=37 => 3+7=10 => 1+0=1
4807526976 => 4+8+0+7+5+2+6+9+7+6=54 => 5+4=9




-13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
233, -144, 89, -55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233

1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8
1, -1, 2, -3, 5, -8, 4, -3, 7, -1, 8, -9, 8

2, 0, 4, 0, 1, 0, 8, 0, 5, 0, 7, 0
2 4 1 8 5 7





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