Cromwell, Peter R.
Cambridge University Press
Cambridge 1997
ISBN: 9780521554329

  [i][c] INDICE:
      Polyhedra in architecture
      Polyhedra in art
      Polyhedra in ornament
      Polyhedra in nature
      Polyhedra in cartography
      Polyhedra in philosophy and literature
      About this book
      The inclusion of proofs
      Approaches to the book
      Basic concepts
      Making models
1.Indivisibile, Inexpressible and Unavoidable
      Castles of eternity
      Egyptian geometry
      Babylonian geometry
      Chinese geometry
      A common origin for oriental mathematics
      Greek mathematics and the discovery of incommensurability
      The nature of space
      Democritus' dilemma
      Liu Hui on the volume of a pyramid
      Eudoxus' method of exhaustion
      Hilbert's third problem
2.Rules and Regularity
      The Platonic solids
      The mathematical paradigm
      Primitive objects and unproved theorems
      The problem of existence
      Constructing the Platonic solids
      The discovery of regular polyhedra
      What is regularity?
      Bending the rules
      The Archimedean solids
      Polyhedra with regular faces
3.Decline and Rebirth of Polyhedral Geometry
      The Alexandrians
      Mathematics and astronomy
      Heron of Alexandria
      Pappus of Alexandria
      Plato's heritage
      The decline of geometry
      The rise of Islam
      Thabit ibn Qurra
      Europe rediscovers the classics
      Campanus' sphere
      Collecting and spreading the classics
      The restoration of the Elements
      A new way of seeing
      Early perspective artists
      Leon Battista Alberti
      Paolo Uccello
      Polyhedra in wodcrafts
      Piero della Francesca
      Luca Pacioli
      Albrecht Dürer
      Wenzeln Jamnitzer
      Perspective and astronomy
      Polyhedra revived
4.Fantasy, Harmony and Uniformity
      A biographical sketch
      A mystery unravelled
      The structure of the universe
      Fitting things together
      Rhombic polyhedra
      The Archhimedean solids
      Star polygons and star polyhedra
      Semisolid polyhedra
      Uniform polyhedra
5.Surfaces, Solids and Spheres
      Plane angles, solid angles, and their measurement
      Descartes' theorem
      The announcement of Euler's formula
      The naming of parts
      Consequences of Euler's formula
      Euler's proof
      Legendre's proof
      Cauchy's proof
      Exceptions which prove the rule
      What is a polyhedron?
      Von Staudt'sproof
      Complementary viewpoints
      The Gauss-Bonnet theorem
6.Equality, Rigidity and Flexibility
      Disputed foundations
      Stereo-isomerism and congruence
      Cauchy's rigidity theorem
      Cauchy's early career
      Steinitz' lemma
      Rotating rings and flexible frameworks
      Are all polyhedra rigid?
      The Connelly sphere
      Further developments
      When are polyhedra equal?
7.Stars, Stellations and Skeletons
      Generalised polygons
      Poinsot's star polyhedra
      Cayley's formula
      Cauchy's enumeration of star polyhedra
      Stellations of icosahedron
      Bertrand's enumeration of star polyhedra
      Regular skeletons
8.Symmetry, Shape and Structure
      What do we mean by symmetry?
      Rotation symmetry
      Systems of rotational symmetry
      How many systems of rotational symmetry are there?
      Reflection symmetry
      Prismatic symmetry types
      Compound symmetry and the S2n symmetry type
      Cubic symmetry types
      Icosahedral symmetry types
      Determining the correct symmetry type
      Groups of symmetries
      Crystallography and the development of symmetry
9.Counting, Colouring and Computing
      Colouring the Platonic
      How many colourings are there?
      A counting theorem
      Applications of the counting theorem
      Proper colourings
      How many colours are necessary?
      The four-colour problem
      What is proof?
10.Combination, Transformation and Decoration
      Making symmetrical compounds
      Symmetry breaking and symmetry completion
      Are there any regular compounds?
      Regularity and symmetry
      Polyhedral metamorphosis
      The space of vertex-transitive convex polyhedra
      Totally transitive polyhedra
      Symmetrical colourings
      Colour symmetries
      Perfect colourings
      The solution of fifth degree equations
I.Appendix I
II.Appendix II
Sources of Quotations
Name Index
Subject Index

1900 1900 2000 2000 1950 2050 Cromwell, Peter R. ( 1964.0507 - ) https://www.liverpool.ac.uk/mathematical-sciences/staff/peter-cromwell/ Cromwell, Peter R. 1864.0507 4518.1024 1997

Generato il giorno: 2018-10-24T03:14:57+02:00 (Unix Time: 1540343697)
Precedente aggiornamento il giorno:0
Prima registrazione il giorno: 2018.1024
Aggiornato una volta

Dimensione approssimata della pagina: 36114 caratteri (body: 34697)

Versione: 1.0.34