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Are there any other kinds of transformations, other than these four (such as projection/inversion of a plane in 3d space?).


Are there scenarios in which your brain thinks it knows what kind of transformation is looking at but it is actually a different one? I guess this is kind of falling into optical illusion territory.


In the lecture, you discussed how these transformations were formalized based on the geometric invariants they preserve, and the algebraic properties followed after. Is this generally the case in more advanced geometry?


What properties would the composition of these transformations have?


Does the order of basic transformation matter?