Ancient chinese pure math : 50 with 49. The arts of “propagate”(fractal) “大衍之数五十，其用四十九”--易经爻辞

The arts of “propagate”(fractal)

If the big size propagate number is 50 that the relatively stationary one is 50, then the relative motion one is 49.

When the big size propagate number is 50, the small size propagate is 5.

The“ 5 ”of 5 actions called 〝 propagate number ″，when the small size propagate is 5. The big size propagate number is 50. Of course ,we also could think the 5 comes from the center 5 of the horse matrix and the tortoise matrix‘s center or the horse matrix and the tortoise matrix‘s center is 5 actions .(They are same thing)

If let the relatively stationary one is 50. Then the relative motion part of the one is 49. In other words, I also could say:

If let the relative motion one is 50. Then the Relatively stationary part of the one is 49. But the two has different direction

Pythagoras theorem express the "50"

As follows：

a=3、b=4、c=5

a²+b²+c²= 9+16+25=50

Pythagoras tree (fractal)

Every time when the Pythagoras tree (fractal) “propagate”--- the relatively stationary one is 50， then the relative motion part of the one is 49.

another 50 with 49：(a+b)²

The (a+b)²〔a is one, b is six〕that (1+6)² expresses the “50”

As follows：

One with six is same root number. if let the “white color” is feminine, One with six containing the amount of feminine the most.

(a+b)²= a²+2ab+ b²

(1+6)²=1²+12 +6²

=49

Any new born one could propagate become mature one relatively like the Pythagoras tree.

Pythagorean theorem expresses the “50”

As follows：

the Square ABDE is 4 orange color equal right triangles plus the center white color little Square .The area of each orange color right triangle is ab ÷ 2 . The center white color little Square's Side length is b-a, then its area is （b－a）²

got ：

　4×（ab ÷ 2）＋（b－a）2=c 2

After Simplification：

　a²＋b²=c²

Any new born one could propagate become mature one relatively like the Pythagoras tree.

When big size propagate number is 50, the small size propagate number is 5.

The big size propagate number is 50 plus the small size propagate number 5 is 55. 50+5=55

if the big size propagate number is 50 ,then the small size propagate number is 5. （the small size propagate number 5 actually is the 5 action.）

When big size propagate number is 50, the small size propagate number is 5. That:

1+2+3+4+5+6+7+8+9+10=55

Odd number is masculine; even number is feminine.

Guy’s total that masculine’s total is 1+3+5+7+9=25 （25 red points）

Girl’s total that feminine’s total is 2+4+6+8+10 = 30 （30 blue points）

Guy’s total that （25 red points）plus Girl’s total（30 blue points）=55

55 is the “horse” matrix “total” number :

1+2+3+4+5+6+7+8+9+10=55

But, if the big size propagate number 50 is not 50 but it is 5000. Then the small size propagate number is 50 now. If the big size propagate number is 5000. The small size propagate number is 50

1+2+3+4+5……+100=5050

If the big size propagate number is 500000. The small size propagate number is 500

1+2+3+4+5……+1000=500500

If the big size propagate number is 50000000. The small size propagate number is 5000

1+2+3+4+5……+10000=50005000

……….

The horse matrix 55 + the tortoise matrix 45 =100

the 100÷2=50 that the 50 is the big size propagate number

（55+45）÷2=50

another 50 with 49：
The proportion expresses the “50”

As follows：

Square with around could have proportion. The circumference of the square is 28. The circumference of the around is 22. The diameter of them is 7 .

28+22≈50

●π代表圆形 ■4 代表方形

●π×7≈21

■4×7=28

21+28≈50

The big size propagate number 50. Its original is the small size propagate number 5.

who is the 5？The 5 was in the center of the “horse” and the “tortoise” or 5 actions .

（transverse looking）of the“I have a stick ,I take it half (or cut it half) every day ,I can't finish it forever and forever”.

↓

Round shape（or universal joint）looking of the“I have a stick ,I take it half (or cut it half) every day ,I can't finish it forever and forever”

↓

Now I take 50 point to do 4 layers .The first layer is the center’s too extreme. The second layer is the future too extreme（any one of the 7 points）

↓

The first layer is the center’s too extreme.

It keep “bear”:
↓

Anyone could be the center’s too extreme relatively.

I randomly fine one and give it an English name that hector.

If I set the hector is the center too extreme as an new “one”

The new comer that hector would “bear” ：

Again，I randomly fine one and give it an English name that Achilles .

The new comer that Achilles would “bear”：

When :
1÷7=0.142857
0.142857 × 1 = 0.142857
0.142857 × 2 = 0.285714
0.142857 × 3 =0.428571
0.142857 × 4 = 0.571428
0.142857 × 5 =0.714285
0.142857 × 6 = 0.857142
0.142857 × 7 = 0.999999=1

The 142857 would keep cycle.

The following I take from “Wikipedia”

http://en.wikipedia.org/wiki/142857_(number)

1 × 142,857 = 142,857

2 × 142,857 = 285,714

3 × 142,857 = 428,571

4 × 142,857 = 571,428

5 × 142,857 = 714,285

6 × 142,857 = 857,142

7 × 142,857 = 999,999

If you multiply by an integer greater than 7, there is a simple process to get to a cyclic permutation of 142857. By adding the first six digits (ones through hundred thousands) to the remaining digits and repeating this process until you have only the six digits left, it will result in a cyclic permutation of 142857

142857 × 8 = 1142856

1 + 142856 = 142857

142857 × 815 = 116428455

116 + 428455 = 428571

142857² = 142857 × 142857 = 20408122449

20408 + 122449 = 142857

Multiplying by a multiple of 7 will result in 999999 through this process

142857 × 7⁴ = 342999657

342 + 999657 = 999999

If you square the last three digits and subtract the square of the first three digits, you also get back a cyclic permutation of the number.

857² = 734449

142² = 20164

734449 − 20164 = 714285

It is the repeating part in the decimal expansion of the rational number 1/7 = 0.142857. Thus, multiples of 1/7 are simply repeated copies of the corresponding multiples of 142857:

1 ÷ 7 = 0.142857

2 ÷ 7 = 0.285714

3 ÷ 7 = 0.428571

4 ÷ 7 = 0.571428

5 ÷ 7 = 0.714285

6 ÷ 7 = 0.857142

7 ÷ 7 = 0.999999

8 ÷ 7 = 1.142857

9 ÷ 7 = 1.285714

The figure could explain the 142857