in the field of technical analysis for stock markets, the usage of so-called Phi-Ellipses is getting popular. One important property of this ellipses is its constant length/width ratio (e.g. 1.618).
Here is an (graphical) example:
Given properties of the ellipse:
- The ellipse is defined by 3 points (point 0, 1 and 2).
- The ellipse has a given length/width ratio (e.g. 1.618).
- Point 0 is the outmost point on the major axis.
I would like to draw the phi-ellipse which fits to points 0, 1 and 2. To do so, I need to calculate the width or length of the ellipse (point 0 is already given).
Does anybody know how to calculate this parameter? (I would like to avoid an iterative algorithm because I think it can be calculated.)
Thank you in advance.