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● The square of 2 is 4; the square of 3 is 9. The halfway point between 4 and 9 is 6.5.
● The square of 4 is 16; the square of 5 is 25. The halfway point between 16 and 25 is 20.5.
● The square of 6 is 36; the square of 7 is 49. The halfway point between 36 and 49 is 42.5.
● The square of 8 is 64; the square of 9 is 81. The halfway point between 64 and 81 is 72.5.
● The square of 10 is 100; the square of 11 is 121. The halfway point between 100 and 121 is 110.5.
● The square of 12 is 144; the square of 13 is169. The halfway point between 144 and 169 is 132.5.
● 2的平方是4;3的平方是9;4與9的中間點是6.5。
● 4的平方是16;5的平方是25;16與25的中間點是20.5。
● 6的平方是36;7的平方是49;36與49的中間點是42.5。
● 8的平方是64;9的平方是81;64與81的中間點是72.5。
● 10的平方是100;11的平方是121;100與121的中間點是110.5。
● 12的平方是144;13的平方是169;144與169的中間點是132.5。
If you examine closely the numbers of the 'square of nine' or the 'odds and evens chart' (see below), you find that these natural squares are aligned on the same angle from the center. The odd squares of 1, 9, 25, 49, 81, and so on, go from the center down to the lower left-hand corner. The even squares of 4, 16, 36, 64, 100, and so on, go from the center up to the top right-hand corner.
如果你仔細檢查一下'square of nine'或'奇偶數表'(如下所示) 中的數字,你將發現這些自然平方數所在位置都會落在以中央點(譯註:不一定是1所在的位置)為圓心的固定角度線上。像1, 9, 25, 49, 81等等這些奇數的平方數都是落在中央點的左下角,像4, 16, 36, 64,100等等這些偶數的平方數都是落在中央點的右上角。
Since the distance from 16 (the square or four) to 25 (the square of five) is 180 degrees around the chart, it becomes clear why Mr. Gann expected changes in the trend of a market price at 180 degrees or 'on an angle of 180'. Similarly, he would expect changes at 90 degrees (one-half of one square) and 360 degrees (two squares).
因為從圖表中16(4的平方)所在的位置到25(5的平方)所在的位置距離180度,所以可以清楚地了解為何甘氏會預測市場價格趨勢的轉折會發生於180度,或者說是’在180度角上’。同樣地,他也預測轉折會發生於90度(半個維度的平方)與360度(兩個維度的平方)。
The square progression seems to work better with three significant digits. If you are studying a market with four digits in a price, try dropping the last number to get to a number you can use on the chart. Similarly, if you are studying a low price stock, try adding a zero or move the decimal to get three significant digits.
利用三位有效數字來處理平方的變化似乎比較好用,如果你正在研究的市場包含四位有效數字,那麼最好去掉最後一個數字,以便得出一個可以讓你用於這個圖表上的數值。
The square of nine is without a one of Mr. Gann's most powerful trading and analysis tools. It also can be a little complex. Re-read this article and we will examine this powerful tool further in the next issue of The New W. D. Gann Technical Review.
無庸置疑,'square of nine'是甘氏最強大的交易與分析工具之一。它也可以變得更複雜一點。重新讀一遍這篇文章,接下來我們將在The New W. D. Gann Technical Review的下一個議題中進一步檢驗這個強大的工具。 |
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