**Equiareal map - Wikipedia**
https://en.wikipedia.org/wiki/Equiareal_map

Every Euclidean isometry of the Euclidean plane is equiareal, but the converse is not true. In fact, shear mapping and squeeze mapping are counterexamples to the converse. Shear mapping takes a rectangle to a parallelogram of the same area. Written in matrix form, a shear mapping along the x-axis is Squeeze mapping lengthens and contracts the sides of a rectangle in a reciprocal manner so that the area is preserved. Written in matrix form, with λ > 1 the squeeze reads

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