神奇的數字，自我實現出來
Magic number, out of self-realization
黃金分割比率，是如何得到的？
Golden ratio is how to get it?
這是一個古代西方數學家與美術家，不約而同，共同發現的數字，
This is an ancient Western Mathematician and Artists, coincidentally, co-discovered the figures,
如果你拿一個長方形的紙：比率長度是1，寬度是0.618，之後，你以寬度，即0.618為邊，在這個長方形裏，切出一個兩邊相等的正方形，剩下的那一邊，很有趣的，也會是另一張，比例為1對0.618的長方形，如此不斷割切，比例永遠一樣，對數學家而言，這只是一個有趣的數字。西方美術家認為，這是美學的分割，一幅畫，畫中的主題，應該放在0.618，這個位置上，才是最完美。
If you take a rectangle of paper: the length ratio is 1, the width is 0.618, after you order width, that is, 0.618 for the side, In this rectangle, the sides cut out a square equal to the remaining side, very interesting they will be another, the ratio 0.618 for the one pair of rectangular, So keep cutting, the ratio is always the same, the mathematician, this is just an interesting number. Western artists believe that this is the aesthetics of the division, a painting, the painting's subject, should be placed 0.618; this position is the most perfect.
黃金分割比率，原本是數學家與美術家，專用的數字，從甚麼時候開始，變成了股市技術分析的技巧，就不得而知。
Golden ratio was originally a mathematician and artist, dedicated to digital, from when to start, into the stock market technical analysis techniques, it is not known.
股票技術分析的專業者，引用這項定律，在股票市場進行股票交易，
Stock technical analysis professionals, citing the law, in the stock market stock trading,
技術分析人員，利用黃金分割定律，探討股價變動中，最高點的位置和最低點的位置，發現準確性很高，
Technical analysts, the use of golden law of price changes, the highest point and lowest point of the position of the location and found a very high accuracy,
由於黃金分割比率，有高度的準確性，所以，股票市場的技術分析人員，利用黃金分割比率，預測未來股票價格變動，主要測試標準之一。
As the golden ratio, a high degree of accuracy, so the stock market technical analysts use Fibonacci ratios to predict future stock price movements, the main test criteria.
其實，這種技術分析學問，只是技術分析人員，自我完成的數據，
In fact, this knowledge of technical analysis, but technical analysts, self-complete data,
當越來越多人，學習技術分析，知道有黃金分割定律，這數字的存在，
When more and more people, learn technical analysis, know the law of the golden section, the existence of this figure,
大眾人士，在股市價格趨勢，上升或下跌到黃金分割比率時，進入股票市場，賣出或買入股票，當有許多人，都不約而同地做相同的行動，表現在股票指數上的趨勢，便會相對地有一致性，所謂神奇數字，如此而已。
People who, in the stock market price trends, up or down to the golden ratio, into the stock market, sell or buy shares, when many people are invariably doing the same action, the performance trend on the stock index, it there will be relatively consistent, the so-called magic number, that's all.
讀者要注意的是：黃金分割比率，只是一個參考工具，不能就此武斷或執著。投資股票，還要參考其他因素和經濟指標。
Readers should note that: golden ratio, is only a reference tool, this cannot be arbitrary or persistent. Invest in stocks, but also of other factors and economic indicators.
另外，黃金分割點和黃金分割區域，是有區別的，不應該教條地，必須等待，黃金分割點的出現，才作出決定，
In addition, the golden section point and the Golden area, there is a difference, should not be dogmatic, must wait, the appearance of golden point, before making a decision,
實際運用中，應該把黃金分割區域的出現，作為決策的依據。
Practical application, should the emergence of the golden zone, as decision-making.
例如，上文提及的人體身材例子。
理論上，測算人體的腰部到頭部的距離，最理想的距離是0.6685，
腰部到腳部的距離，最好是1,805。
但是，實際中，絲毫不差真正達到此標準的，可以說根本不可能。
因此，只要人的腰部到頭部的距離，大約在0.6685區域，腰部到腳部的距離，大約在1.0815區域，就相當標準了，事實上也會令人覺得舒服。
黃金分割比率在生活上的應用
一條線段分割為A、B兩部份，使其中A線段的一部份，與原有線段全長之比例，相等於B線段那一部份，與A線段這部份之比例。
A line segment divided into A, B two parts, so that one part of the segment A, the ratio of the original line length equal to that part of segment B, and A portion of this line ratio.
有趣的是，這個數字在自然界和人們生活中隨處都可以見到：
Interestingly, this figure in nature and in people's lives can be seen everywhere:
人們肚臍的位置，正好是人體身高的黃金分割點，
People navel position, just the body height of the golden point,
人體的膝蓋，由肚臍到腳跟，正是黃金分割點。
Human knee, the navel to the heel, it is golden point.
² 人的標準體溫是37度，室內溫度是25度，這是人們感受最舒適的溫度，
進行計算之後：25÷37=0.676很接近0.618。
Ø Golden ratio, in other areas of application:
People's standard temperature is 37 degrees; the indoor temperature is 25 degrees, which is that people feel the most comfortable temperature.
After the calculations: 25 ÷ 37 = 0.676 is very close to 0.618.
After the calculations: 25 ÷ 37 = 0.676 is very close to 0.618.
² 電腦顯示屏的長度與寬度比值，大約為1.6。經過計算之後：1/0.618=1.618。
Ø The length and width of the computer screen ratio of about 1.6. Calculated after: 1/0.618 = 1.618.
² 人們理想的體重計算，十分接近：身高×（1－0.618）。
Ø The ideal body weight, are very close: height × (1-0.618).
² 人們每一天上班工作8小時：8×0.618=4.944。
Ø People go to work eight hours each day: 8 × 0.618 = 4.944.
² 人們上班工作第5個小時之後，正是最需要休息的時候，同時也是期待下班回家的時候。
Ø People go to work 5 hours later, it is most in need of rest, but also expect to come home from work.
² 小學生每一節上課的時間是40分鐘，而他們的注意力只有：
40×（1－0.618）=15.28分鐘，
因此，教師必須把握，學生學習的情緒。
Ø Each section of students in class time is 40 minutes, while their attention only:
40 × (1-0.618) = 15.28 minutes.
Therefore, teachers must grasp the mood of students.
² 建築師們對數字0.618也特別偏愛，
無論是古埃及的金字塔，或者是近世紀的法國，都有與0.618有關的資料。
Ø Architects are particularly preferred for digital 0.618,
Whether it is the ancient pyramids of Egypt,
Or Notre Dame or the Eiffel Tower in France the last century, have the relevant information with 0.618.
² 人們還發現，一些著名的油畫、雕塑、攝影作品的主體位置，大多數放置在畫面的0.618處。
Ø It also found that some well-known painting, sculpture, photography of the subject position, the majority placed in screen 0.618.
² 音樂家們一致認為，管絃樂器的絃線，放在琴弦的0.618處，能使發出的音樂聲響，更加柔和甜美。
Ø Musicians agreed that the orchestra's string line device, on the strings of 0.618, can send the music sound more soft and sweet.
認識重要的黃金分割比率，基本位置，然後
Understanding of important golden ratio, the basic position, and then
利用黃金分割比率，找出合適的交易價格。
Golden ratio, can find the right trading price.
A. 0.382：
0.382在黃金分割比率裡面，所代表的意義，就是在一個上升波段，回調的第一個重要支撐位置或是一個下跌波段，反彈的第一個重要壓力位置；
Inside the golden ratio 0.382, represents the meaning is in a rising band, the first important support callback location or a drop-band, a significant rebound in the first pressure position;
我們都知道當一個趨勢在運行的過程中，是不會一口氣的直奔終點的，
We all know that when a trend in the running process, not the straight end of the breath,
這種運行當中，都會有一些回調的震盪，
This operation which will shock some of the callback,
而當一個趨勢在運行的時候，我們去判別這個趨勢，是否一個強勢的趨勢，就可以利用，回調幅度的大小，來做一個很有效的判斷，
When a trend in the run, we to judge this trend is a strong trend, you can use the callback rate of size, to do a very effective judge,
假設，一個趨勢的波動過程中，其回調幅度，沒有跌穿0.382的位置，
Assumptions, fluctuations in the course of a trend, the callback rate, did not fall to below 0.382 positions,
那麼就意味，這是一個強勁的趨勢，也代表這個趨勢，尚未結束，價位稍為整理後，這個趨勢，將有極大的機會，再創出新高點或新低點。
Then it means that this is a strong trend, but also on behalf of this trend is not over yet, after finishing the price slightly, this trend will have a great opportunity for another new highs or new lows.
B. 0.5：
0.5在黃金分割比率裡面，所代表的意義，
0.5 In the golden ratio which, by the meaning,
就是在一個上升趨勢裡面，回調的過程中，第二個重要支撐位置或是一個下跌趨勢中，反彈的第二個重要支持位置；
There is a rising trend, the callback process, the second important support position or a down trend, the rally to support the second important position;
當一個趨勢，到達暫時的頂點或低點時，在這過程中，出現了回調0.5的幅度，通常表示，市場可能會出現，比較長時期的調整期，
When a trend, reaching a temporary peak or low, in the process, the magnitude of 0.5 occurred callback, usually indicates the market may appear relatively long period of adjustment,
行情出現震盪的機會，短時期內，再創新高點或出現新低點的機會降低，
Shock in market opportunities, a short time, a new high or new low-point opportunities to reduce,
但整體的市場運行現況，仍以原先的趨勢為主要方向。
However, the status of the overall operation of the market, the trend is still the main direction of the original.
C. 0.618：
0.618在黃金分割比率裡面，所代表的意義：
0.618 In the golden ratio which, by the meaning,
這是在一個上升趨勢中，股票價格，回調期間，最重要阻力位置；或是一個下跌趨勢中，反彈期間，最重要支持位置；
This is a rising trend in stock prices, during the callback, the most important resistance levels; or a decline in the rebound period, the most important support for the position;
若一個趨勢的運行，出現了回調0.618的幅度，
If the operation of a trend, there has been a callback rate of 0.618,
代表股票市場的運行，出現反轉趨勢的可能性大增，
Representative of the stock market run, the trend reversal, the possibility of greatly increased,
一旦下跌趨勢，向上突破0.618的回調幅度，或上升趨勢，向下跌破0.618的回調幅度
Once the downward trend, break up the callback rate of 0.618, or an upward trend, the callback rate down below the 0.618
那麼便顯示，不論上升趨勢或下跌趨勢，正式完結。
Then it shows an upward trend or downward trend in both the formal end.
股票市場隨著的運行，將會以全新的型態移動。
With the stock market run, will be a new type of mobile.
黃金分割比率，在投資過程的運用：
Golden ratio, the use of the investment process:
黃金分割比率，在眾多的技術分析工具裡面，可以算是，參考價值最高的一種，也是我個人最喜愛使用的技術分析工具，
Golden ratio in many technical analysis tools which can be regarded as the reference value of the highest kind, but also my personal favorite use of technical analysis tools,
我個人認為，0.382、0.5、0.618 這三個黃金分割比率，特別重要；
Personally, I think, 0.382, 0.5, 0.618 three golden ratio, is particularly important;
黃金分割比率的應用、不需要設置任何工具，簡單容易使用，而且非常有效果，尤其是在計算成交量巨大的股票或指數，具有十分神奇的效果，
Golden ratio of applications, without setting any tools, simple and easy to use and very effective, especially in large volume in the calculation of the stock or index, has a very magical effect,
黃金分割比率有高效果的原因，我可以解釋為：因為黃金分割比率，蘊含着宇宙間的自然定律，
金融市場裡，所有的交易，都由人所促成，所以人類的交易行為，也不會跳出大自然的定律。
Golden ratio has a high effect of reasons, I can be explained as follows: because golden ratio contains the natural laws of the universe.
Financial markets, all transactions, led by the people, so the human transactions it will not jump out of the law of nature.
Financial markets, all transactions, led by the people, so the human transactions it will not jump out of the law of nature.
事實上，在我們的生活環境中，到處可以看見，符合黃金分割比率的生活體驗。
In fact, in our living environment, can be seen everywhere, meet the golden ratio of life experience.
例如：我們到處可以看見的香煙包裝盒子、雜誌的長度和寬度比例；普通樹葉的寬度與長度之比例；蝴蝶身體長度與翅膀展開後，兩者長度的比例，也是接近0.618。
For example: we can see everywhere, cigarette packaging boxes, magazines, the length and width ratio; ordinary leaf width and length ratio; butterfly body length, with wings expanded, the ratio between the length is close to 0.618.
美麗的事物如：金字塔、巴黎鐵塔，甚至所謂俊男美女的臉型，或身材，也都符合黃金分割比率，
Beautiful things such as: Pyramids, the Eiffel Tower, even the so-called attractive men and women face, or body, are also in line with the golden ratio,
再從更玄妙的角度來看，地球上陸地的面積，和海洋面積，兩方面的比較，都接近0.618。
More mysterious from the perspective of Earth's land area, and marine area, two aspects of the comparison, are close to 0.618
人們睡眠所需的時間，與日間生活所需的時間，兩者比較；人類身體的溫度和最舒適溫度的比較，都極度接近黃金分割比率0.618
The time required for people to sleep, and daytime life time, in comparison; human body temperature and the most comfortable temperature comparisons are extremely close to the golden ratio 0.618
學習使用黃金分割比率，很多人，無法把黃金分割比率運用得很好，主要原因是找不到正確的高點和低點，
Learning to use the golden ratio, a lot of people cannot use the golden ratio very well, mainly due to not find the right high and low points,
當我們要運用黃金分割比率，分析指數時，必須採用數據的最高價位，和最低價位，在這個時候，投資者，最容易犯的兩個錯誤是：
When we use the golden section ratio analysis index, the data must be the highest price, and the lowest position, at this time, investors most likely to commit two errors are:
在股價預測中，有兩種黃金分割比率的分析方法：
In the stock price prediction, there are two golden ratio analysis methods:
第一種方法：找尋近期指數趨勢中，指數上升的頂端位置，或下跌的最低位置，用來計算，未來走勢的基礎，
The first method: find the recent trend in the index, rose to the top position, or drop the lowest position, used to calculate the future movements of the foundation,
當股價上升時，選擇上升起點的股價，作為計算基礎，當上升趨勢，到達黃金分割比率時，股價因為受到阻力，持續上升的趨勢，可能發生逆轉。
When the stock price rises, selects the starting point of the stock, as calculated on the basis, when the upward trend to reach the golden ratio, the stock price because of resistance, and the rising trend could be reversed.
當股價下跌時，選擇下跌前，最高的股價，作為計算基礎，當下跌趨勢，到達黃金分割比率時，股價因為受到支持，持續下跌的趨勢，可能發生逆轉。
When stock prices fall, the choice fell before the highest stock price, as calculated on the basis, when the downward trend to reach the golden ratio, the share price since been supported and sustained downward trend could be reversed.
第二種方法：
股價下跌趨勢發生逆轉後，股價運行的趨勢，由下跌轉為向上攀升。處理辦法
舉例：
當下跌趨勢逐漸緩慢下來時，假設某A股的最低價格是１０元，那麼，股價有機會逆轉攀升時，投資人可以預先計算出各種不同的阻力價位：
The second method:
Stock price decline, reversed, the trend of stock prices run from fall to rise up, when this happens, the approach taken:
For example:
Stock price decline, reversed, the trend of stock prices run from fall to rise up, when this happens, the approach taken:
For example:
When the downward trend gradually slow down, assuming the minimum A-share price is $ 10, then have the opportunity to reverse the rise in stock prices, investors can pre-calculate a variety of different resistance levels:
$１０×（１＋１９．１％）＝$１１．９
$１０×（１＋３８．２％）＝$１３．８
$１０×（１＋50.0％）＝$15
$１０×（１＋６１．８％）＝$１６．２
$１０×（１＋８０．９％）＝$１８．１
$１０×（１＋１００％）＝$２０
$１０×（１＋１１９．１％）＝$２１．９
然後，投資者，審視股價在市場實際變動的情形，作出對應措施。
Then, investors look at price changes in actual market situation, make the corresponding measures.
² 當上升趨勢逐漸緩慢下來時，假設B股的最高價格是30元，那麼，股價有機會逆轉下跌時，投資人可以預先計算出，各種不同的支持價位：
Ø When the upward trend gradually slow down, the assumption B share the maximum price is $ 30, then have the opportunity to reverse the falling stock price, investors can be calculated in advance, supported by a variety of different price points:
$３０×（１－１９．１％）＝$２４．３
$３０×（１－３８．２％）＝$１８．５
$３０×（１－0.5％）＝$15
$３０×（１－６１．８％）＝$１１．５
$３０×（１－８０．９％）＝$５．７
然後，依照實際趨勢，演變的情形，再作最後決定。
Then, follow the actual trends, the evolution of the situation, making the final decision.
黃金分割比率，由於沒有理論作為根據，所以有人批評這是迷信，是巧合，但自然界，的確充滿一些奇妙的巧合，一直難以說出道理。
Golden ratio, because there is no theory as a basis, it has been criticized as a superstition, is a coincidence, but nature is indeed full of some amazing coincidence, has been difficult to tell truth.
艾略特的波浪理論，都是採用黃金分割比率的理論，成為世界聞名的波浪理論，廣泛地為投資人士所採用。
Elliott wave theory, are based on the golden ratio theory, as the world famous wave theory, widely used for the investors.
神秘數字是否真的只是巧合呢？
Mysterious figure is really just a coincidence?
還是大自然一切生態，都可以用神秘數字作為解釋呢？
Or the nature of all ecological can be used to explain it as a mysterious figure?
這個問題，只能見仁見智。但黃金分割比率，在投資市場上，無人不知，無人不用，作為一個投資者，不能不深入研究，只是，不能太過執著。
This problem can only be a matter of opinion. But the golden ratio, in the investment market, no one does not know, no one not in use, as an investor, cannot fail to in-depth study, but not too persistent.
能夠快人一步，採取適當行動的投資人士，將會更加穩操勝券。
To quick step, to take appropriate action investors will be more surer of success.
認識五個基本的黃金分割率數值
Five basic understanding of the value of the golden ratio
黃金分割比率數值：0.191、0.382、0.5、0.618、0.809，可以分割為五個黃金分割點，
Golden ratio values ; 0.191, 0.382, 0.5, 0.618, 0.809, can be divided into five golden points,
根據這個數值，從股價近期走勢中，找出最高點或最低點，作為計算基數，這樣的做法，便能找到，即將出現的支撐位置或阻力位置。
According to this value, from the recent share price movements, find the highest or lowest point, as the calculation base, such an approach, can be found, the upcoming location of the support or resistance.
不過，要注意的是：找尋最高點與最低點的數值，是需要結合，時間運動規律來確認的。
Note, however, is: find the highest and lowest points of value, is the need to combine the time to confirm the law of motion.
因為市場隨時會出現波動，有時，是時間週期首先出現，有時，是價位首先出現，兩個因素，都有可能同時出現。
Because the market will always fluctuate, sometimes, is the time period first appeared, and sometimes, the price comes first, two factors are likely to occur simultaneously.
當時間、價格同時出現，那麼，就意味着，將會有大幅度的運行趨勢，極有可能形成，大級別的趨勢移動。
When the time, the price simultaneously, then it means there will be substantial run trend is likely to form, the trend of moving large level.
（A）當股市上升時，投資者最關心的，是上升的頂點，會停留在甚麼位置？
When the stock market rises, investors are most concerned about is the rise of the vertices will stay in what position?
事實上，影響股價變動的因素很多，要想準確地，掌握上升行情的最高價，是絕對不可能的事情，
In fact, many factors affect the stock price changes, in order to accurately grasp the highest increase in market price, it is absolutely impossible,
因此，投資人所能做的，就是依照黃金分割律，計算可能出現的股價反轉點，以供實際操作時的參考。
Therefore, investors can do, is to follow the golden rule to calculate the stock price reversal points that may arise, for the actual operation of the reference.
當股價向上升期間，逐漸脫離低位點，
When the stock price to rise during the period, moving away from the low point,
從上升的速度與持久性，依照黃金分割律，它的漲勢會在上漲幅度，接近或達到0.382與0.618時，會發生變化。
From the rising speed and persistence, according to the golden rule, it gains in the rate of increase, close to or reach 0.382 and 0.618, it will change.
也就是說，當上升接近或超越38.2%或61.8%時，就會出現相反壓力，有違反上升趨勢，轉變為下跌的現象，換言之，暫時停止，上升的走勢。
That is, when close to or exceeds the 38.2% increase, or 61.8%, there will be pressure on the contrary, in violation of the rise, fall into the phenomenon, in other words, to temporarily stop rising trend.
應用黃金分割律，除了固定的0.382與0.618，是上漲趨勢過程中，相反走勢的轉接點，
Application of Golden Section, in addition to a fixed 0.382 and 0.618, the trend is rising process, the opposite trend of the transfer point,
其中，也要注意，這一小距離的相反走勢轉接點，即0.382的一半，也就是0.191，也是重要的依據。
One should also note that this small transfer point from the opposite trend, that is half of 0.382, which is 0.191, is also an important basis.
因此，當股市上升趨勢開始時，要預測股價上升的動力及相反走勢轉接點時，
Therefore, when the stock market upward trend began, the power to predict stock prices rise and the opposite trend of transfer points,
將即場股價行情，下跌的最低點，乘以0.191、0.382、0.809與1，作為上升的幅度的預測。
The spot market price fell to its lowest point multiplied by 0.191, 0.382, 0.809 and 1, as the forecast rate of increase.
當股價上漲幅度越過1倍，走勢轉接點，以1.191、1.382、1.809和2倍，進行計算。依此類推。
When the stock price rises over 1 times, the trend transfer point to 1.191, 1.382, 1.809, and 2-fold, calculated. And so on.
例如，當股票指數下跌趨勢結束時，假設A股票的最低價為4元，（股票上升趨勢的起步點）
For example, when stock indexes decline at the end of the stock's lowest price assumption A $ 4（Starting point for the upward trend in stock）
那麼，當股價逆轉上升時，投資人可以預先計算出來，各種不同狀況，股價上升的轉接點，
也就是：
Then, when the stock price reversal to rise, investors can pre-calculate a variety of different circumstances, rising trend of switching points.
That is:
That is:
4×(1+0.191)=4.764元；
4×(1+0.382)=5.528元；
4×(1+0.618)=6.472元；
4×(1+0.809)=7.236元；
4×(1+1.0)=8元；
4×(1+1.191)=8.764元。
投資者計算出數據後，再根據實際股票價格變動的情形，然後採取，是進攻或是退出的決定。
Investors calculate the data, then the stock price movements based on the actual situation, then take, offensive or out of the decision.
（B）當股市下跌時，投資者最關心的，是下降的低點，會停留在甚麼位置？
(B) When the stock market declines, investors are most concerned about is the low down, what will remain in place?
影響股市下跌的因素極多，投資人根本無法完全掌握。不過，投資者可以從黃金分割比率，計算跌勢進行中，的支持價位，增加投資人，能夠用低位的價格，買進股票。
Factors that affect stock prices very much, investors cannot fully grasp. However, investors from the golden ratio to calculate the decline in progress, the support price, increased investor can use the low price, buy the stock.
當股價下跌時，股票價格，逐漸脫離高點，
從下跌趨勢的速度和持久性，依照黃金分割比率的理論，當下跌趨勢的幅度，接近或達到0.382與0.618時，便會發生變化。也就是說，當下跌幅度，接近或超越38.2%或61.8%時，隨時會發生逆轉。換言之，股票價格，雖然在下跌趨勢中，但是卻出現了支持力，下跌趨勢有可能反轉上升，結束下跌行情的可能。
When prices decline, the stock price, moving away from the high point, Downward trend from the speed and persistence, according to golden ratio theory, when the magnitude of the downward trend, close to or reach 0.382 and 0.618, they will change. That is, when decreased, close to or exceeds 38.2% or 61.8%, at any time is reversed. In other words, stock prices, although in decline, but it appeared to support, could reverse the downward trend rise, ending the possibility of market decline.
下跌趨勢行情展開時，除了0.382和0.618有支持之外，在0.191、0.809位置，都有可能發揮，強大支持的力量。
Market decline started, in addition to 0.382 and 0.618 with support, in 0.191, 0.809 position, are likely to play a strong supporting force.
例如，上升行情結束前，（A）股最高價格是$3，那麼，股票價格下跌時，投資人，可以計算各種不同的支持價位，也就是：
For example, before the end of rising prices, (A) share the highest price is $ 3, then stock prices fall, investors can calculate a variety of support price, which is:
3×(1-0.191)=$2.427；
3×(1-0.382)=$1.854；
3×(1-0.618)=$1.46；
3×(1-0.809)=$0.573。
在大多數的情況下，將黃金分割比律，運用於股票市場，投資人會發現，在大趨勢的判斷上，它的有效性，高於使用在個別股票上。
In most cases, than the golden rule, applied to the stock market, investors will find that, in judging the trend, its validity, than the use of the individual stocks.
這是因為，個別股票的投機性較強，有部分股票，會有幕後的經理人，某些股票，極容易出現急促上升或急促下跌的趨勢，這樣，如果利用，刻板的計算公式，尋找頂點與低點，其中的準確性就會降低。
This is because the strong speculative individual stocks, some stocks, there will be the manager behind the scenes, some stock, very prone to rapid increases or rapid downward trend, so that if the use of a rigid formula, find the vertex and low, which will reduce the accuracy.
使用黃金分割比率，預測股票指數的趨勢，相對來說，會較為準確。雖然，也會存在人為因素，但與個別股票比較，受到的影響，要緩和得多。因此，掌握最高點與最低點的準確性，機會也會大一些。
Using the golden ratio, predict the trend of stock indices, relatively speaking, would be more accurate. Although there will be human factors, but compared with individual stocks, impact, much more to ease. Thus, taking the highest and lowest points of accuracy, the opportunity will be larger.
大部份的投資者，每一次，當股市調整至，0.618這一個水平時，把金錢投入股票市場，進行買入或賣出，你這麼做，他這麼做，這個黃金分割比率，就變成了「神奇」數字了。
Most investors, and each time, when the stock market to, a level of 0.618 which, to put their money into the stock market, to buy or sell, you do so, he did, the golden ratio, it becomes a "magic" figures.
從數學到美術到股市，投資，也都成為一門藝術呢？
From mathematics to fine arts to the stock market, investment, have also become an Art?
（B）當股市下跌時，投資者最關心的，是下降的低點，會停留在甚麼位置？
(B) When the stock market declines, investors are most concerned about is the low down, what will remain in place?
影響股市下跌的因素極多，投資人根本無法完全掌握。不過，投資者可以從黃金分割比率，計算跌勢進行中，的支持價位，增加投資人，能夠用低位的價格，買進股票。
Factors that affect stock prices very much, investors cannot fully grasp. However, investors from the golden ratio to calculate the decline in progress, the support price, increased investor can use the low price, buy the stock.
當股價下跌時，股票價格，逐漸脫離高點，
從下跌趨勢的速度和持久性，依照黃金分割比率的理論，當下跌趨勢的幅度，接近或達到0.382與0.618時，便會發生變化。也就是說，當下跌幅度，接近或超越38.2%或61.8%時，隨時會發生逆轉。換言之，股票價格，雖然在下跌趨勢中，但是卻出現了支持力，下跌趨勢有可能反轉上升，結束下跌行情的可能。
When prices decline, the stock price, moving away from the high point, Downward trend from the speed and persistence, according to golden ratio theory, when the magnitude of the downward trend, close to or reach 0.382 and 0.618, they will change. That is, when decreased, close to or exceeds 38.2% or 61.8%, at any time is reversed. In other words, stock prices, although in decline, but it appeared to support, could reverse the downward trend rise, ending the possibility of market decline.
下跌趨勢行情展開時，除了0.382和0.618有支持之外，在0.191、0.809位置，都有可能發揮，強大支持的力量。
Market decline started, in addition to 0.382 and 0.618 with support, in 0.191, 0.809 position, are likely to play a strong supporting force.
例如，上升行情結束前，（A）股最高價格是$3，那麼，股票價格下跌時，投資人，可以計算各種不同的支持價位，也就是：
For example, before the end of rising prices, (A) share the highest price is $ 3, then stock prices fall, investors can calculate a variety of support price, which is:
3×(1-0.191)=$2.427；
3×(1-0.382)=$1.854；
3×(1-0.618)=$1.46；
3×(1-0.809)=$0.573。
在大多數的情況下，將黃金分割比律，運用於股票市場，投資人會發現，在大趨勢的判斷上，它的有效性，高於使用在個別股票上。
In most cases, than the golden rule, applied to the stock market, investors will find that, in judging the trend, its validity, than the use of the individual stocks.
這是因為，個別股票的投機性較強，有部分股票，會有幕後的經理人，某些股票，極容易出現急促上升或急促下跌的趨勢，這樣，如果利用，刻板的計算公式，尋找頂點與低點，其中的準確性就會降低。
This is because the strong speculative individual stocks, some stocks, there will be the manager behind the scenes, some stock, very prone to rapid increases or rapid downward trend, so that if the use of a rigid formula, find the vertex and low, which will reduce the accuracy.
使用黃金分割比率，預測股票指數的趨勢，相對來說，會較為準確。雖然，也會存在人為因素，但與個別股票比較，受到的影響，要緩和得多。因此，掌握最高點與最低點的準確性，機會也會大一些。
Using the golden ratio, predict the trend of stock indices, relatively speaking, would be more accurate. Although there will be human factors, but compared with individual stocks, impact, much more to ease. Thus, taking the highest and lowest points of accuracy, the opportunity will be larger.
大部份的投資者，每一次，當股市調整至，0.618這一個水平時，把金錢投入股票市場，進行買入或賣出，你這麼做，他這麼做，這個黃金分割比率，就變成了「神奇」數字了。
Most investors, and each time, when the stock market to, a level of 0.618 which, to put their money into the stock market, to buy or sell, you do so, he did, the golden ratio, it becomes a "magic" figures.
從數學到美術到股市，投資，也都成為一門藝術呢？
From mathematics to fine arts to the stock market, investment, have also become an Art?
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