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=54060° 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=81090° 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=972108° 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=1080120° 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=1215135° 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=1260140° 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

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

 O S I R I S Press for swim.. R A