Abstract
I n his Harvard lecture on the aesthetics of music, Leonard Bernstein emphasised the fundamental role played by transformation, while he described the compositions of Mozart, Beethoven and Mahler as paralinguistic patterns of repetition and variation. In passing, he claimed the same would be found true for the other arts. We can immediately confirm that this is clearly true in visual art, in which we find a fundamental presence of certain geometric transformations: projective transformations in pictorial art and symmetry transformations in ornamental art. Conversely, mathematical studies of geometric transformations are frequently of great visual interest [1]-this is certainly so for the two geometric mappings that I propose to discuss here, inversion and antiMercator. Our discussion starts by recalling in a systematic way the list of elementary plane transformations, enabling us to reach inversion and antiMercator at ninth and eleventh places. Later we shall bring in threedimensional considerations.
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