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.

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

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...

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.