The projective dimensional analysis based on the projective extension of sc
aling group and projective dimensional function is presented. We study the
notion of self-similarity based on the physical quantities and not on topol
ogy. The projective analog of the classical theorem-pi has been formulated
in terms of (projective) numerical invariants. The additivity dimensions re
placing fractal dimension are briefly discussed. Intuitive examples illustr
ate presented ideas. (C) 2001 Elsevier Science Ltd. All rights reserved.