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We report on a novel use of parallel coordinates as a pedagogical tool for illustrating the non-intuitive properties of high dimensional spaces with special emphasis on the phenomenon of Curse of Dimensionality. Also, we have collated what we believe to be a representative sample of diverse approaches that exist in literature to conceptualize the Curse of Dimensionality. We envisage that the paper will have pedagogical value in structuring the way Curse of Dimensionality is presented in classrooms and associated lab sessions.