# Doubling fib ratios and other expansions

FX:AUDUSD   Australian Dollar / U.S. Dollar
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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.
Basically I think as long as you get both fib expansions (1.618) and doubles (x2), there should be a lot of connections.
I have to admit I'm experimenting with the ratios. I use them with arcs, and when it comes to arcs SCALE is very important. If the scale is not right for the arcs, you would be better off using ellipses than circles. My study on GBPUSD arcs making sense shows how accurate and repetitive arcs can be.
I use .472 because it works with the ratios.
If A=1.618 or the "fib multiplier" then .236*A=.382 and .236*2=.472, then .382*fib=.618 and .382*2=.764, .618*fib=1 also .618*2=1.236.
Then to 1/sine 45 (1.4142) the cosecant ...618*1.4142=.874 and .874*fib(1.618)=1.236 (the same value as .618 *2...just a reverse manipulation). Cosecant ratios make 2X the distance every 2nd one.
I may switch to total fibs and doubles. Right now I'm experimenting with the cosecant values also.
I was also looking at how these ratios may interrelate with actual angles from their ratios. ie. If you takes the arcsine of all those ratios it also produces interesting angle relations. Sine ratio because you're dealing with the distance on the arc (hypotenuse) or y/r. Just an interesting test.
Actually .5*cosecant (1.4142)= the sine ratio .7071 for a 45 degree angle or arctan 45=1
Robert24
I can see, you're pretty much advanced in trigonometrical math. I hope you'll find some practical application for all of those ratios. In the heat of the battle you've got to have them ready in place to refer to. Too much of ratios may be detrimental to you trading decisions, because you'll find yourself wondering which one to rely upon. My advice is have your method as objective as possible and - in your final trading toolbox - as few ratios as possible.
ForceFollower
You're right there can be too many ratios happening. Just like too many angles. I was trying out the 1/2 value of .382. It hits quite a bit also. .191*2=.382 and .236*2=.472 and .382*2=.764 and .618*2=1.236 so you've got fibs and doubles. Should cover some ground. Like I mentioned. I'm just experimenting with the cosecant ratios for now. My most reliable method is actually channels, like TXN at the very bottom of my published. I find the scale is one of the most crucial things to set right for everything syncing. The angles work, the right diagonals work, the arcs work (instead of ellipses) and the channels bring it together for the band of movement. I also use cycles sometimes but not continuous cycles of the same distance. I find just using boxes for 2 cycle sizes helps.
Robert24
Great. I didn't know that all those reliable ratios, when halfed, produced other reliable ratios. I don't know of any merits of the .191 and .472, but .382, .764 and 1.236 are good indeed, esp. .382. And the word "halfed" - you say "doubled" - I'd go "halfed", because for me 0.500 is also very important, both in projections (ie. alternate price projections) and (internal) retracements.

I wish you all the best. Make steady progress and you'll achieve the mastery. Just keep in mind though, that everything works sometimes and nothing works all the time. So the key is to find what works most often...
Well, I just use these Fib ratios: 0.854, 0.764, 0.618, 0.382, 0.236, 0.146. Plus: all of them added to 1, 2 and 3, eg.: 1.618, 2.236 etc.
Quite surprisingly, during my 5.5-year experience with trading fx I've found that the two most powerful ratios in the markets are: 0.382 and 0.500 - the latter not even being a Fib ratio at all. :-) However, I don't understand why use any other derivative of Fib ratios, like .786 or .886 - I find them superfluous.
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