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
5 - Reflections on the mirror
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
Beauty! Where shall one begin on a subject so vast, one that has stirred so many celebrated writers? What a theme! An endless one; and let it be said in passing, just such questions as these are the most interesting, because with them, the last word is never said and because everyone can have a different opinion.
E. Delacroix (1938: 705)Why so many examples of symmetry in man-made objects? Does symmetry add beauty? Certainly, the implied consequence of an affirmative answer to the latter, namely the fact that the more symmetries an object possesses the more beautiful the object is, cannot be true. For the plane itself is the most symmetrical of all objects and yet it is wanting life. But then how does symmetry relate to beauty?
These questions do not have a definite answer. Yet, such a lack of definition appears not to have hindered attempts at formulating answers, and it could be argued that it has, in fact, provided a reason for multiple efforts to do so. For beauty itself has been the subject of many philosophical reflections and its perception studied as a branch of psychology. It would perhaps be as foolish to endeavour a description of all this pondering as it would be blind to ignore it. A possible compromise consists of selecting those reflections whose nature best suits the purpose of this book and whose contents will, therefore, throw light on our subsequent exposition. In doing so we will be oblivious to most of the discussion around beauty, including arguments which are close to our theme.
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- Information
- Manifold MirrorsThe Crossing Paths of the Arts and Mathematics, pp. 111 - 127Publisher: Cambridge University PressPrint publication year: 2013