Vài lời về TT tuần mới !

Em đọc rồi chỉ thấy Fibonaci chứ không có Fibinacci.

đọc kỹ đi tôi không chê bất cứ ai ! Còn pác giỏi thì đi sang topic đúng mà đọc nhé ! Pác có thói kiêu ngạo nói năng luẩn quẩn ! Sang chỗ khác mà tham khảo vào đây làm gì ? Học hỏi là cả một bến bờ và không bao giờ hết !

Giỏi dịch hộ cái :
Chapter 9

Fibonacci Numbers and the Golden Ratio

Recall that a list of numbers

a1, a2, a3, ?, an, ?..

is called a sequence of numbers. So, the first term of ths sequence is a1, the second term of the sequence is a2, and so on.



Definition: The sequence

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

is called the Fibinacci sequence and these numbers are called the Fibinacci numbers. So,


The first term of the sequence is F1 = 1


The 2nd term of the sequence is F2 = 1


The 3rd term of the sequence is F3 = 2


The 4th term of the sequence is F4 = 3


The 5th term of the sequence is F5 = 5


The 6th term of the sequence is F6 = 8


The 7th term of the sequence is F7 = 13


The 8th term of the sequence is F8 = 21


The 9th term of the sequence is F9 = 34


The 10th term of the sequence is F10 = 55


The 11th term of the sequence is F11 = 89


The 12th term of the sequence is F4 = 144

??

N) In general, FN denotes the Nth-term of the sequence.



What is the value of FN? To answer that you have to understand the pattern of the sequence. Note that


2 = F3 =1 + 1 = F1+ F2


3 = F4 =1 + 2 = F2+ F3


5 = F5 =2 + 3 = F3+ F4


8 = F6 =3 + 5 = F4+ F5


13 = F7 =5 + 8 = F5+ F6


21 = F8 = 8 + 13 = F6+ F7


34 = F9 =13 + 21 = F7+ F8


55 = F10 = 21 + 34 = F8+ F9


89 = F11 =34 + 55 = F9+ F10


144 = F12 =55 + 89 = F10+ F11



So, we observe that, except for F1 and F2, each term is the sum of the two preceding terms. So, we have

F1 =1 F2 = 1 and FN = FN-2+ FN-1 (for N>2).



Suggested Problems: Ex. 1,2,3,5,6 (pp. 318).



The Formula: The Fibonacci numbers can be directly computed by the Binet''s Formula:



FN= (((1 + 5 1/2)/2)N + ((1 - 5 1/2)/2)N)/ 5 1/2



Definition: The number f = (1 + 5 1/2)/2 is called the golden ratio. According to the calculator, approximately, (correct up to a certain decimal point)

f = 1.618033989.



Let us also define another number t = (1 - 5 1/2)/2. According to the calculator, approximately, (correct up to a certain decimal point)

t = - 0.6180339887.



Remark 1: Note that these two numbers f, t are solutions of the quadratic equation x2 = x+1.



Remark 2: One can also check that fN = FNf+FN-1.



Remark 3: This golden number f and the Fibonacci numbers appear in nature and geometry, art, architecture. Your textbook went through a very interesting discussion on this. It will be an interesting reading for you.



Some Geometry

Definition: A gnomon to a figure A, is a connected figure B, which, when suitably attached to A produces a new figure which is similar to A. If "G&A" is similar to A then G is a gnomon to A.



Recall, in geometry, we say two figures are similar if one is a scaled version of the other. We will have further discussion on gnomons in the class. This part will not be available on the web.



Suggested Problems: Examples 1-10 Ex. 28-32 (pp. 321).

Ngưỡng cản 500 quá lớn tuy nhiên diễn biến giaodịch của phiên thứ 6 tuần trước có thể thấy rõ một số tổ chức không muốn thị trường giảm trong lúc này. Vì nếu bây giờ giảm thì VNindex sẽ giảm một mạch, theo mình trước hết là mốc 450, nếu tiếp tục đổ dốc thì là 400. Thị trường phụ thuộc hoàn toàn vào thứ 2 và thứ 3. Tôi đoán thứ 2 sẽ chưa giảm mạnh đâu, sẽ phân hóa, cổ phiếu tốt có thể biến động rất ít nhưng cổ phiếu lởm sẽ giảm sàn. Thị trường ngày thứ 2 phải giảm điểm nhẹ và khối lượng giao dịch lớn. Thứ 3 tiếp tục giảm nhẹ và khối lượng khớp tiếp tục khủng. Nếu được như vậy, thứ 4 và thứ 5 là cơ hội để lên tàu một số cổ phiếu tốt.
Hiện giờ TK tôi chỉ còn VSP chiếm 50% tổng giá trị tài khoản. Thứ 6 vừa rồi hú tim định chạy nhưng tính đi tính lại thì thấy còn cơ hội để ăn thêm VSP nên liều. Thứ 2 quan sát rồi đưa quyết định chính thức. Trong một thị trường giảm điểm thì cổ phiếu tốt cũng đi. Mà hiện nay, theo mình vĩ mô chưa được sáng sủa lắm, tiếng là lạm phát tăng chậm lại nhưng lũy kế từ đầu năm đến tính tổng đã lên bao nhiêu rồi, còn mấy tháng cuối năm nữa. Sang 2009 chắc không thoát cái vụ thuế rồi, tiền NH thì vẫn chưa thừa mứa cho chứng khoán đâu, nhu cầu vay vốn còn nhiều lắm.
Nếu cho mình đoán thì chọn 80% cho một xu hướng điều chỉnh giảm về 400 còn 20% cho một xu hương tăng lên 520. Mà mình thì thích xuống hơn.

fibinacci array in class õ?Âõ?Âõ?Âõ?Â
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FIBONACCI STUDIES


Overview
Leonardo Fibonacci was a mathematician who was born in Italy around the year 1170. It is believed that Mr. Fibonacci discovered the relationship of what are now referred to as Fibonacci numbers while studying the Great Pyramid of Gizeh in Egypt.

Fibonacci numbers are a sequence of numbers in which each successive number is the sum of the two previous numbers:


1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 610, etc.

These numbers possess an intriguing number of interrelationships, such as the fact that any given number is approximately 1.618 times the preceding number and any given number is approximately 0.618 times the following number. The booklet Understanding Fibonacci Numbers by Edward Dobson contains a good discussion of these interrelationships.
Interpretation

There are four popular Fibonacci studies: arcs, fans, retracements, and time zones. The interpretation of these studies involves anticipating changes in trends as prices near the lines created by the Fibonacci studies.

Arcs

Fibonacci Arcs are displayed by first drawing a trendline between two extreme points, for example, a trough and opposing peak. Three arcs are then drawn, centered on the second extreme point, so they intersect the trendline at the Fibonacci levels of 38.2%, 50.0%, and 61.8%.

The interpretation of Fibonacci Arcs involves anticipating support and resistance as prices approach the arcs. A common technique is to display both Fibonacci Arcs and Fibonacci Fan Lines and to anticipate support/resistance at the points where the Fibonacci studies cross.

Note that the points where the Arcs cross the price data will vary depending on the scaling of the chart, because the Arcs are drawn so they are circular relative to the chart paper or computer screen.

The following British Pound chart illustrates how the arcs can provide support and resistance (points "A," "B," and "C").



Fans

Fibonacci Fan Lines are displayed by drawing a trendline between two extreme points, for example, a trough and opposing peak. Then an "invisible" vertical line is drawn through the second extreme point. Three trendlines are then drawn from the first extreme point so they pass through the invisible vertical line at the Fibonacci levels of 38.2%, 50.0%, and 61.8%.. (This technique is similar to Speed Resistance Lines.)

The following chart of Texaco shows how prices found support at the Fan Lines.



You can see that when prices encountered the top Fan Line (point "A"), they were unable to penetrate the line for several days. When prices did penetrate this line, they dropped quickly to the bottom Fan Line (points "B" and "C") before finding support. Also note that when prices bounced off the bottom line (point "C"), they rose freely to the top line (point "D") where they again met resistance, fell to the middle line (point "E") and rebounded.

Retracements

Fibonacci Retracements are displayed by first drawing a trendline between two extreme points, for example, a trough and opposing peak. A series of nine horizontal lines are drawn intersecting the trendline at the Fibonacci levels of 0.0%, 23.6%, 38.2%, 50%, 61.8%, 100%, 161.8%, 261.8%, and 423.6%. (Some of the lines will probably not be visable because they will be off the scale.)

After a significant price move (either up or down), prices will often retrace a significant portion (if not all) of the original move. As prices retrace, support and resistance levels often occur at or near the Fibonacci Retracement levels.

In the following chart of Eastman Kodak, Fibonacci Retracement lines were drawn between a major trough and peak.



You can see that support and resistance occurred near the Fibonacci levels of 23 and 38%.

Time Zones

Fibonacci Time Zones are a series of vertical lines. They are spaced at the Fibonacci intervals of 1, 2, 3, 5, 8, 13, 21, 34, etc. The interpretation of Fibonacci Time Zones involves looking for significant changes in price near the vertical lines.

In the following example, Fibonacci Time Zones were drawn on the Dow Jones Industrials beginning at the market bottom in 1970.



You can see that significant changes in the Industrials occurred on or near the Time Zone lines.

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