[...]... 0. 618 or Square root of the 0.786 ( ) • 1. 13 = Fourth root of 1. 618 or Square root of the 1. 27 ( ) • 1. 27 = Square root of the 1. 618 ( ) ) Complementary Derived Ratios: 0.382 = ( 1- 0 . 618 ) or 0. 618 2 0.50 = 0.7072 0.707 = Square root of 0.50 ( ) 1. 41 = Square root of 2.0 ( ) 2.0 = (1+ 1) 2.24 = Square root of 5 ( ) 2 2. 618 = 1. 618 3 .14 = Pi (See later section “The Importance of Pi (3 .14 ) in Harmonic Trading )... = 1 inch ( ) Section B = 0. 618 inches ( Section C = 0.382 inches A – B = C ) ( + _ ) B = A | -| -| | | 1 - 0. 618 = 0.382 + 0. 618 = 1 Chapter 2 Fibonacci Numbers 13 These line segments can be divided in various combinations to manifest phi (0. 618 ) ratios • Ratio of A to B = 1/ 0. 618 = 1. 618 • Ratio of A to C = 1/ 0.382 = 2. 618 (1+ 1. 618 ) • Ratio of B to A = 0. 618 /1. .. yields 1. 618 55/34 = 1. 6764 71 ~ 1. 618 Repeating the process, the next division of the tenth calculation (34+55=89) over the ninth calculation ( 21+ 34=55) equals 1. 618 182 or 1. 618 89/55 = 1. 618 182 ~ 1. 618 These mathematical relationships remain constant throughout the entire Fibonacci series to infinity In the realm of Mathematics, the 1. 618 is known as the golden ratio or Phi The inverse (1/ 1. 618 ) of... sequence requires a minimum of eight calculations (0 +1= 1)… (1+ 1=2)… (1+ 2=3)…(2+3=5)…(3+5=8)… (5+8 =13 )…8 +13 = 21) 13 + 21= 34)…( 21+ 34=55)…(34+55=89) After the eighth sequence of calculations, there are constant mathematical ratio relationships that can be derived from the series Starting with the sum of the eighth calculation (34) as 11 12 Harmonic Trading: Volume One the numerator and using the sum of the ninth... (1+ 1. 618 ) • Ratio of B to A = 0. 618 /1 = 0. 618 • Ratio of B to C = 0. 618 /0.382 = 1. 618 • Ratio of C to A = 0. 618 /1 = 0. 618 • Ratio of C to B = 0.382/0. 618 = 0. 618 The golden section is closely related to the golden ratio since the ratios have a relationship to one another that is equal to phi (0. 618 ) or the inverse, Phi (1. 618 ) Ancient Examples The 0. 618 and the 1. 618 constants from the series are found... understand that Harmonic Trading ratios are unique The following list comprises the only ratios that are utilized to determine precise Harmonic patterns 18 Harmonic Trading: Volume One Harmonic Trading Ratios Primary Ratios: (Directly derived from the Fibonacci Number Sequence) • 0. 618 = Primary Ratio • 1. 618 = Primary Projection Primary Derived Ratios: • 0.786 = Square root of the 0. 618 ( • 0.886 =... 0. 618 retracement 20 Harmonic Trading: Volume One Primary Bearish Retracement: 0. 618 Again, the 0. 618 is probably the best-known Fibonacci ratio It is important to note that Elliott Wave measurements frequently utilize 0. 618 retracements to project time and price targets The bearish 0. 618 retracement (see Figure 2.6) frequently can be found in well-established down-trend channels In addition, long-term... revolution around the sun As we all know, the Earth requires 365 days to complete one revolution If you divide 225 by 365, the result is approximately 0. 618 of a year (225/365 = 0. 616 ~ 0. 618 ) and the inverse (365/225 = 1. 622 ~ 1. 618 ) results in 1. 618 of a year Fibonacci Rectangles and Shell Spirals Another illustration that exemplifies the Fibonacci numeric sequence starts with one small square of 1. .. overall appeal of trading Such diverse cross-market appeal has furthered the need for trading strategies to maintain a stringent unbiased perspective and analyze price behavior without favor For these reasons, the Harmonic Trading approach has emerged as a reliable and effective system of rules to navigate any market Harmonic Trading: Volume Two Since this book is titled Harmonic Trading: Volume One, the... Air [Pomeroy, WA: Lambert-Gann Publishing, 19 27], 78) In this manner, it is important to focus on the application of the strategies that consistently work and not attempt to seek the deep philosophic justifications for their validation Chapter 2 Fibonacci Numbers 17 Harmonic Trading Ratios Utilizing Phi (1. 618 ) and its inverse (0. 618 ) as the primary measurement basis, Harmonic Trading techniques identify . Cataloging-in-Publication Data Carney, Scott M., 19 6 9- Harmonic trading / Scott M. Carney. v. cm. Contents: v. 1. Profiting from the natural order of the financial — ISBN -1 3 : 97 8-0 -1 3-7 0 515 0-2 (v. 1. the publisher. Printed in the United States of America First Printing April 2 010 ISBN -1 0 : 0 -1 3-7 0 515 0-6 ISBN -1 3 : 97 8-0 -1 3-7 0 515 0-2 Pearson Education LTD. Pearson Education Australia PTY, Limited. Pearson. pbk. : alk. paper) ISBN -1 0 : 0 -1 3-7 0 515 0-6 (v. 1 : pbk.) 1. Investment analysis. 2. Investments. 3. Portfolio management. I. Title. HG4529.C368 2 010 332.63’2042—dc22 20090 510 44 It is with the sincerest