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P. Boughton (2003) - Real Gann Angles.(pdf)

The diagonal of a square with a base of 1 is 1.414, or square root of 2, or a 45 degree angle. The S&P 500 high in 1994 482, time 1.414 = 681 which was the next high in the SP in the middle of 1996. So we can say 681 is 45 degrees from 4 price angle. And, 681 x 1.414 = 964 is another 45 degree price angle. (Editor's note: 482 x 1.414 x 1.414 = 482 x 2 = which is the same as 482 at a 60 degree angle.) | The Real Gann Angles by Paul Boughton (http://www.ensignsoftware.com/tips/tradingtips44.htm) The diagonal of a square with a base of 1 is 1.414, or square root of 2, or a 45 degree angle. The S&P 500 high in 1994 was 482, time 1.414 = 681 which was the next high in the SP in the middle of 1996. So we can say 681 is 45 degrees from 482, a price angle. And, 681 x 1.414 = 964 is another 45 degree price angle. (Editor's note: 482 x 1.414 x 1.414 = 482 x 2 = 964, which is the same as 482 at a 60 degree angle.) Now lets add some other angles. The diagonal of a 1x1x1 cube is the square root of 3. The square root of 4 is 2 or a 60 degree angle, and so on. The square root of 10 is approximately pi. The diagonal of a 3x1 rectangle is almost a 72 degree angle. 482 x square root of 10 = 1524. 482 x pi = 1514. 482 at a 72 degree angle is 1559 which is the all time S&P high of 1552. On the flip side of the S&P mountain, the square root of the 1552 high is 39.40, divided by 1.414 = 27.89, resquared = 776. 39.43 x 1.414 = 55.7 x 1.414 = 78.8 x 1.414 =111.4. Oops that’s our time series of natural trading days for the 0.618 row in the table in the first article! Taking it to another level of understanding, the first time vibration was 291 bars which at 60 degrees is 582 bars or the time of the July 2002 low. And 1552 at 60 degrees is 776 which was the July 2002 price low. So we can say that price and time met at 60 degrees. There are angles in price and angles in time and when they meet change is inevitable. Price and time are .