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Arithmetic and Geometry
The Birth of Mathematics in the Antiquity: Arithmetic and Geometry.
From the Antiquity to Middle Age, Classical Art represented the space "as it is" in its “frozen” and rigid Euclidean structure. In this historical period Platonic Solids and the Golden Mean were the “prototypes of beauty and harmony”; the underlying Geometry was of course the “Euclidean Geometry”, that describes the “ordinary space” together with its geometrical properties.
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Perspective and Symmetry
Development of Mathematics from Renaissance to '900: Perspective and Symmetry.
The Art of Renaissance was dominated by Perspective and represented the space “as it appears to the eye”, still on a Euclidean basis. Euclidean Geometry appeared as the only paradigm to represent Space and was considered as the basic geometric structure of Nature. The transition from Greek’s Euclidean Geometry to the Geometry of Perspective was related to the conception of “beautiful painting”; canons of beauty and harmony dominated Art and the notion of Symmetry became more and more important.
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Curvature, Motion, Relativity and Chaos
Mathematics in the XX Century: Curvature, Motion, Relativity and Chaos.
Modern Art represents the World “as it is perceived by the mind”. In Mathematics we have with Riemannian Geometry the dissolution of an absolute space in favor of many private ones, dominated by non-linearity, curvature, extra dimensions and dynamics. Time and Motion pervade artistic expressions, while new experiments lead to the introduction of Chaos and Fractality also in Art. New Digital Technologies give eventually a further impetus to Art and allow a more and more important crossroad between Art & Science.
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