Holdings Information

Bibliographic Record Display

• Title:Manifold mirrors : the crossing paths of the arts and mathematics / Felipe Cucker, City University of Hong Kong.
  
•    
• Author/Creator:Cucker, Felipe, 1958-
  
• Published/Created:Cambridge : Cambridge University Press, 2013.
  

• Holdings

  Holdings Record Display

  • Location:MAA LIBRARY (IKB) stacksWhere is this?
    
  • Call Number: NX180.M33 C83 2013
    
  • Number of Items:1
    
  • Status:Available
    

   
• Library of Congress Subjects:Arts--Mathematics.
  
• Description:x, 415 pages : illustrations (chiefly color) ; 26 cm
  
• Notes:Includes bibliographical references and indexes.
  
• ISBN:9780521429634 (hardback)
  0521429633 (hardback)
  9780521728768 (paperback)
  0521728762 (paperback)
  
• Contents:Machine generated contents note: A.1. Martini
  A.2. On their blindness
  A.3. Musical Offering
  A.4. garden of the crossing paths
  1. Space and geometry
  1.1. nature of space
  1.2. shape of things
  1.3. Euclid
  1.4. Descartes
  2. Motions on the plane
  2.1. Translations
  2.2. Rotations
  2.3. Reflections
  2.4. Glides
  2.5. Isometries of the plane
  2.6. On the possible isometries on the plane
  3. many symmetries of planar objects
  3.1. basic symmetries
  3.1.1. Bilateral symmetry: the straight-lined mirror
  3.1.2. Rotational symmetry
  3.1.3. Central symmetry: the one-point mirror
  3.1.4. Translational symmetry: repeated mirrors
  3.1.5. Glidal symmetry
  3.2. arithmetic of isometries
  3.3. representation theorem
  3.4. Rosettes and whirls
  3.5. Friezes
  3.5.1. seven friezes
  3.5.2. classification theorem
  3.6. Wallpapers
  3.6.1. seventeen wallpapers
  3.6.2. brief sample
  3.6.3. Tables and flowcharts
  3.7. Symmetry and repetition
  3.8. catalogue-makers
  4. many objects with planar symmetries
  4.1. Origins
  4.2. Rugs and carpets
  4.3. Chinese lattices
  4.4. Escher
  5. Reflections on the mirror
  5.1. Aesthetic order
  5.2. aesthetic measure of Birkhoff
  5.3. Gombrich and the sense of order
  5.4. Between boredom and confusion
  6. raw material
  6.1. veiled mirror
  6.2. Between detachment and dilution
  6.3. blurred boundary: I
  6.4. amazing kaleidoscope
  6.5. strictures of verse
  7. Stretching the plane
  7.1. Homothecies and similarities
  7.2. Similarities and symmetry
  7.3. Shears, strains and affinities
  7.4. Conics
  7.5. eclosion of ellipses
  7.6. Klein (aber nur der Name)
  8. Aural wallpaper
  8.1. Elements of music
  8.2. geometry of canons
  8.3. Musical Offering (revisited)
  8.4. Symmetries in music
  8.4.1. geometry of motifs
  8.4.2. ubiquitous seven
  8.5. Perception, locality and scale
  8.6. bare minima (again and again)
  8.7. blurred boundary: II
  9. dawn of perspective
  9.1. Alberti's window
  9.2. dawn of projective geometry
  9.2.1. Bijections and invertible functions
  9.2.2. projective plane
  9.2.3. Kleinian view of projective geometry
  9.2.4. Essential features of projective geometry
  9.3. projective view of affine geometry
  9.3.1. distant vantage point
  9.3.2. Conics revisited
  10. repertoire of drawing systems
  10.1. Projections and drawing systems
  10.1.1. Orthogonal projections
  10.1.2. Oblique projections
  10.1.3. On tilt and distance
  10.1.4. Perspective projection
  10.2. Voyeurs and demiurges
  11. vicissitudes of perspective
  11.1. Deceptions
  11.2. Concealments
  11.3. Bends
  11.4. Absurdities
  11.5. Divergences
  11.6. Multiplicities
  11.7. Abandonment
  12. vicissitudes of geometry
  12.1. Euclid revisited
  12.2. Hyperbolic geometry
  12.3. Laws of reasoning
  12.3.1. Formal languages
  12.3.2. Deduction
  12.3.3. Validity
  12.3.4. Two models for Euclidean geometry
  12.3.5. Proof and truth
  12.4. Poincare model of hyperbolic geometry
  12.5. Projective geometry as a non-Euclidean geometry
  12.6. Spherical geometry
  13. Symmetries in non-Euclidean geometries
  13.1. Tessellations and wallpapers
  13.2. Isometries and tessellations in the sphere and the projective plane
  13.3. Isometries and tessellations in the hyperbolic plane
  14. shape of the universe
  Appendix: Rule-driven creation
  Compliers/benders/transgressors
  Constrained writing.