Book contents
- Frontmatter
- Contents
- Mathematics: user's manual
- Appetizers
- 1 Space and geometry
- 2 Motions on the plane
- 3 The many symmetries of planar objects
- 4 The many objects with planar symmetries
- 5 Reflections on the mirror
- 6 A raw material
- 7 Stretching the plane
- 8 Aural wallpaper
- 9 The dawn of perspective
- 10 A repertoire of drawing systems
- 11 The vicissitudes of perspective
- 12 The vicissitudes of geometry
- 13 Symmetries in non-Euclidean geometries
- 14 The shape of the universe
- Appendix: Rule-driven creation
- References
- Acknowledgements
- Index of symbols
- Index of names
- Index of concepts
9 - The dawn of perspective
Published online by Cambridge University Press: 05 May 2013
- Frontmatter
- Contents
- Mathematics: user's manual
- Appetizers
- 1 Space and geometry
- 2 Motions on the plane
- 3 The many symmetries of planar objects
- 4 The many objects with planar symmetries
- 5 Reflections on the mirror
- 6 A raw material
- 7 Stretching the plane
- 8 Aural wallpaper
- 9 The dawn of perspective
- 10 A repertoire of drawing systems
- 11 The vicissitudes of perspective
- 12 The vicissitudes of geometry
- 13 Symmetries in non-Euclidean geometries
- 14 The shape of the universe
- Appendix: Rule-driven creation
- References
- Acknowledgements
- Index of symbols
- Index of names
- Index of concepts
Summary
Oh, che dolce cosa è questa prospettiva!
Paolo Uccello, quoted in (Vasari, 1991: 83)Perspective is to Painting what the bridle is to a horse, and the rudder to a ship.
Leonardo da Vinci (2002: §113)Figure 9.1 shows a photograph taken by Edward Weston in 1937 of a tomato field on the Monterey Coast of California. The multitude of tomato shrubs draws a pattern that we quickly identify (disregarding imperfections on the placement of individual shrubs) as a wallpaper and it is the contrast between this pattern and the gently irregular landscape of the hill in the background that, most probably, first attracts the eye.
This impression of regularity that we identify with a wallpaper pattern is, however, put to test by the fact that the image does not evenly spread the shrubs: those in the lower part are separated by bigger distances in the surface of the photograph than those close to the hill. This is certainly in contrast with the wallpapers shown, for instance, in Figures 3.12, 3.13, 4.20 and 6.5.
The reasons for this disagreement come quickly to mind, and one may express them with several wordings: the distances in the plane where the tomato shrubs grow are not respected in the plane of the picture, distant objects appear smaller than ones close to the observer, or (encompassing the previous phrases in a common expression) the picture shows the landscape in perspective.
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- Manifold MirrorsThe Crossing Paths of the Arts and Mathematics, pp. 225 - 259Publisher: Cambridge University PressPrint publication year: 2013