Editing Möbius transformation (section)

=== Loxodromic transforms ===
The transform is said to be ''loxodromic'' if <math>\operatorname{tr}^2\mathfrak{H}</math> is not in {{nowrap|[0, 4]}}. A transformation is loxodromic if and only if <math>|\lambda|\ne 1</math>.

Historically, [[navigation]] by [[loxodrome]] or [[rhumb line]] refers to a path of constant [[bearing (navigation)|bearing]]; the resulting path is a [[logarithmic spiral]], similar in shape to the transformations of the complex plane that a loxodromic Möbius transformation makes. See the geometric figures below.