You've lost me when you moved from image 4 to image 5.

If you provide a brief bit of text describing each addition, you'd be approaching a geometrical proof.

In the step 4 to 5 you've added a white triangle, but no corresponding explanations or measurements.

if you could please a) enlarge the diagram slightly to more easily show additional measurements and provide additional explanations & measurements.

Every angle, every length should be identified. If you wish to use A, B, C, a, b, c and provide the numericals in a legend, that'd be fine.


Without these however, I, for one, remain lost at step 4 to step 5 with the addition of the white triangle.

From the last two images, I gather you are attempting to relate it to the GP. That's vaguely interesting (could be more so) but if there is the relation you are implying then you should be able to connect each picture to the next via a brief (1-2 sentence) explanation and literally proof your way into the GP on the same diagram as the original 1,2, sqrt(5) triangle.

Which, btw, has an official mathematical name I cannot recall at the moment (not the 1,2,3 triangle either)