Editing Complex number (section)

====Shapes====
Three [[collinearity|non-collinear]] points <math>u, v, w</math> in the plane determine the [[Shape#Similarity classes|shape]] of the triangle <math>\{u, v, w\}</math>. Locating the points in the complex plane, this shape of a triangle may be expressed by complex arithmetic as
<math display=block>S(u, v, w) = \frac {u - w}{u - v}. </math>
The shape <math>S</math> of a triangle will remain the same, when the complex plane is transformed by translation or dilation (by an [[affine transformation]]), corresponding to the intuitive notion of shape, and describing [[similarity (geometry)|similarity]]. Thus each triangle <math>\{u, v, w\}</math> is in a [[shape#Similarity classes|similarity class]] of triangles with the same shape.<ref>{{cite journal |last=Lester |first=J.A. |title=Triangles I: Shapes |journal=[[Aequationes Mathematicae]] |volume=52 |pages=30–54 |year=1994 |doi=10.1007/BF01818325 |s2cid=121095307}}</ref>