Fibonacci ratios are actually 1.618339887 or it's inverse =.618033988769. FIB*FIB=2.618 is also an important ratio. If you multiply each one of the ratios by it some interesting hits happen also. 2.618/2=1.309 another multiplier that comes up. .764*1.309=1 Actually it's .763932022462*1.30901699444=1 according to what I get.
For the stockmarket things are just rounded. Sine 45 ratio expansions are 1/(sine 45)= 1.41421356237 or the cosecant.
This might show the ratios better. I actually prefer .472 to .5 but for explanation here's how they join. .236, .382, .618, 1, and 1.618 are all fib expansions...and Fib*fib=2.618
The .764 comes from .382*2.
2*.236=.472 and 2*.382=.764 and 2*.618=1.236.
Then there are expansions from sine 45 (.7071)
Sine 45=.707106781187 and the inverse of that number = 1.41421356237 (cosecant). Now just keep multiplying by that ratio and you get 2 next. (double of 1).
So ... .7071, 1, 1.4142, 2, 2.8284, etc. This doubles every 2nd expansion.
.618*cosecant ratio (1.4142)=.874 and .874*cosecant=1.236 which is the same as .618*2=1.236, then .874*fib=cosecant 1.4142
Interesting relations. Basically expansions on fibs, doubles and cosecant of sine 45.
In real application I look for the .764 arc to go with the 1 arc more than others. Sometimes .72 and 1 also work.
If you set up the chart for right diagonals 1st, then the circles also tend to work better, otherwise they probably should be more elliptical shaped, in which case all these ratios would be inaccurate.
For the stockmarket things are just rounded. Sine 45 ratio expansions are 1/(sine 45)= 1.41421356237 or the cosecant.
This might show the ratios better. I actually prefer .472 to .5 but for explanation here's how they join. .236, .382, .618, 1, and 1.618 are all fib expansions...and Fib*fib=2.618
The .764 comes from .382*2.
2*.236=.472 and 2*.382=.764 and 2*.618=1.236.
Then there are expansions from sine 45 (.7071)
Sine 45=.707106781187 and the inverse of that number = 1.41421356237 (cosecant). Now just keep multiplying by that ratio and you get 2 next. (double of 1).
So ... .7071, 1, 1.4142, 2, 2.8284, etc. This doubles every 2nd expansion.
.618*cosecant ratio (1.4142)=.874 and .874*cosecant=1.236 which is the same as .618*2=1.236, then .874*fib=cosecant 1.4142
Interesting relations. Basically expansions on fibs, doubles and cosecant of sine 45.
In real application I look for the .764 arc to go with the 1 arc more than others. Sometimes .72 and 1 also work.
If you set up the chart for right diagonals 1st, then the circles also tend to work better, otherwise they probably should be more elliptical shaped, in which case all these ratios would be inaccurate.