Figure 4.2  Different Values of \upsilon

 

This is another graph by Strange and this one shows four different values:  \upsilon=\frac{\pi}{2.2}\:, \:\frac{\pi}{3}\:,\:\frac{\pi}{4}\:, \:\frac{\pi}{6}
The curves have different extents along the x axis, which is the \lambda angle.

In order to represent \upsilon as a quantity that expresses direction, the curves must be “normalized” by making the extent of the curves along the x axis equal to 1, ¬†similar (mathematically and conceptually) to the way vectors are normalized in order to create a unit vector or direction vector.

Once the curves are normalized, they express direction as a function of direction, without any length.