, :

1. , .
2. ( , ).
3. .

() :



, , , 1170 . 1250 . ( Guilielmo) , .

, , **** , , , , , .

1200 . , , , . , , .


(Liber Abaci) 1202:


( ) .
, .

9, ( Algorism) , .


:


: 1, 2, 3, 4, 5, 6, 7, 8, 9 , 0 () ( Zephirum ) , .

, .

, , , .

, , , .

, , , .


:


, 1202.


:


. ɿ , , ɿ


:


:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55,........ . , . .

1228 .

( Practica Geometriae) .

1225 ( Liber Quardratorum) , , , (Book of Squares) .




( ) :


. .

, , : 23.6%, 38.2%, 50%, 61.8% 100%. .


:



:


0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 , 233, 377, 610......... .


, :


0 + 1 = 1
1 + 1 = 2
2+ 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 5 = 13
13 + 8 = 21

.

, , , 1.618 , .





(61.8%) ( Golden Mean- The Golden Ratio) :


61.8% , , , :

8 / 13 = 0.6153 13 / 8 = 1.625

1.625 * 0.6153 = 1

55 / 89 = 0.6179 89 / 55 = 1.618

1.618 * 0.6179 = 1

, 61.8 100.

, , 161.8 , 1.618 0.618 1.

23.6% :



0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

8 / 34 = 0.2352 23.6

38.2% :



0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

55 / 144 = 0.3819 38.2

, 50% 78.6% . 50% , 50%.


ȿ


, , , .

, : , , (Daisy) 34, 55, 89 .

, , .

1.618, 0.618, , , 1.618, .

, :

, 1.618. ! .


ɿ


: , . , , 1.618, .





, , , .

, .

, 23.6% , 38.2 % , 50% , 61.8%, 100%


Ϳ


, , , , 45 .





, .


:


1. .

2. , .

3. , .

4. .

5. 23.6% , 38.2 % , 50% , 61.8%, 100%

6. , , .


:


1. , , , .

2. , , , , . , .

3. , , .


4. , .

5. , , ( Fibonacci Retracements).

6. , , , .

7. , . .

8. ( ), .


, , .

, , ,