Difference between y-length and h-length

OB = 1

The difference between y-length and h-length of BA, relative to O, as the line BA approaches infinity.

AOB and BOC are similiar triangles. As the length BA and OA approach being infinitely long, the length OC approaches the length OB, which is 1. Likewise, as the angle AOB approaches 90°, the angle at OBC approaches 90°.

If e^{ylength - hlength} = OB + OC, then as
BA approaches infinity, OB + OC approaches 2.

e^{ylength - hlength} = 2 (as BA approaches infinity)

y-length - h-length = ln2

y-length - h-length = .693147181

As the length BA approaches being infinitely long, the difference between the y-length and the h-length of AB, relative to O, approaches .693147181, the square root of 2.