The author examines the meaning of the title question, noting that geometry can be described as the study of those properties of a shape that remain unchanged even if it is subjected to some transformation. He deals here with 2-D homogeneous coordinates, so the transformation is the standard homogeneous projective transformation representable by a 3*3 matrix. Any two shapes that can transform into each other using such a matrix are counted as the same shape. He then describes what he has determined so far and gives a list of questions he has that are unresolved.
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