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Griffiths H. — Surfaces
Griffiths H. — Surfaces

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Название: Surfaces

Автор: Griffiths H.

Аннотация:

This book is an attempt to break that cycle, being designed for students
who might later teach children. It has two aspects, one mathematical, and
one educational. Mathematically, it expounds the topology of compact
surfaces as far as the Classification Theorem, and treats also the Morse
Theory of such surfaces. In fact the whole treatment is a 'handle-body'
approach. However, a conventional mathematical treatment would begin
4logically' with topological spaces, continuity and homeomorphisms,
before settling down to combinatorial ideas. Any student who could not
jump the initial conceptual thresholds would then be cut off from the rich
intuitive material that underlies the later work. And it is the rich intuitive
material that a future teacher will need, for introducing children to
3-dimensional thinking, so that he can stress the meaning rather than the
syntax.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 120

Добавлена в каталог: 20.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A-level      102 104
Absolute (maximum, minimum)      89
Addition equations      57 59
Addition theorem      48 57
Agreement 1      32
Agreement 2      33 96
Agreement 3      34 96
Agreement 4      39 96
Agreement 5      39 45
Agreement 6      53 97
Agreement 7      67 96
Amoeba      43 111
Analysis (subject)      97
Analysis, case-by-case      102
Annulus      9 35 69 73 76 99
ARC      22 67 97
Arc succession      25 32
Arrow (orienting)      28 44 79 110
Assembly Theorem      76 94 100
Assembly, ordered      75
Associativity      102
Axioms      ix 100
bar      83 86
Bay      39
Beetle      17
Big Question      30 58
Bijection      101 102
Boundary      7 81 100
Bridge      17 50
Bridge, multi-      25
Bridge, twisted      17 52
Calculus      101 104
Cayley      82
Characteristic      18 100
Classification Theorem      61
Closed surface      7 54 61 94
Cocoon      34 66 69 73 101
Colouring problems      69 73
Compact      96 104 106
Complex (paper)      64 76 86
Connected      76 96
contour      85 86
Corner      7
Counter-example      103
Critical level      89 91
Critical point      85 89
Cross-cap      54 61
Crystal      6
cube      7 64
Curve (Jordan)      10 14 86 95 100 103
Cylinder      9
definitions      34 99
Differential invariant      66
dodecahedron      8 64
Double torus      27 107
Dual      64
Duality (Alexander)      100
Ear      15 48
Ear, multi-      24
Ear, twisted      16 48
Earthworm      43 111
EDGE      7; free 7
Equation: mountaineer's      82
Equation: of hyperboloid      106
Equation: of surface      12
Equation: of torus      12 106;
Equation: quadratic      64 103
Euler      18 66
Euler formula      66
Euler number      18 59 65 72 82 103 110
Examinations      103 104
Experiment      46 102
Family      32 58 96
Finer      71
Five-colour Theorem      69
Flange      36
Flood      83
flowchart      81 104
Fount (of type)      101
Four-colour Conjecture      69
Free (edge)      7
Fundamental theorem      58
Gallic Plan      61
Gallic Theorem      58
Genus      27 99
Graph theory      7 99
Handle      27 42 51 61
Heawood's Theorem      73
Height      82 94 104
Homeomorphism      95 96 105 106
Hyperboloid      106
icosahedron      8 64
Induction, mathematical      59 68 101 102
Invariance      63
Invariance Theorem      65 94
Invariant      65 75 81
Isomorphism      101
Isthmus      83 86
JORDAN      10
Jordan curve      10 14 86 95 100 103
Jordan curve theorem      95 100
Klein      21
Klein bottle      54 73
Lamina      32 68
Left-handed      10 41 99
Level      85 89
Lid      21 26
Linear graph      7 99
Manifold      98; generalized 96
MAP      69
Mathematical induction      59 68 101 102
Mathematical language      97 101
Mathematical model, modelling      95 96 104
Mathematical surface      95
Maximum      85 89
Maxwell, J.C.      82
Meaning      ix
Minimum      85 89
Model      102
Moebius      10
Moebius band (or strip)      10 37 44 54 69 73 95
Moebius equation      13
Morse theory      82 98
Morse, M.      82
Morse, S. F B.      82
Mountaineer's equation      82
Multiplicity      25
Mystery surface      76 96
Non-orientable      29 61 79 94
Number: Euler      18 59 65 72 82 103 110
Number: orientability      60 66 75 80
Number: real      22 95 103
octahedron      8 64
Order of assembly      62 63 75
Ordered assembly      75
Orientability number      60 66 75 80
Orientability Theorem      78
Orientable      29 44 79 80 110
Oriented      29
Ovaloid      3
Overpass      15 41 99
Panel      2 32 66 95
Paper complex      64 76 86
Paper surface      7 94
Paper surface, Gallic      61
Paper surface, mystery      76 96
Paper surface, non-orientable      29 61 79 94
Paper surface, orientable, oriented      29 44 79 80 110
Paper surface, with boundary      10
Parity      60 103
PASS      82 84 89
Pass, over-      99
Pass, under-      99
Peak      82 84 89
Pedagogical Axiom      ix 100
Pit      82 84 89
Plan      39 44 58 101 102
Planar region (or surface)      14 39 41
Planting a concept      101 104
Plateau      82 85
Plato      7
Platonic polyhedra      8 34 64
Platonic solids      7
Polygonal Jordan Curve Theorem      95
Polyhedron, regular      8 76
Prescription      45
prism      9
Projective geometry      22
Projective plane      22 54 73
Proof (notion of)      x 31
Proper panelling      64 78
Punctured Klein bottle      21 38 44
Punctured projective plane      22
Punctured sphere with g handles      26 27
Punctured torm      21 17
Quadratic equation      64 101
Question (Big)      30 58
Rcpanelling      25 63 65 71
Recognition Claim      54
refinement      71
Regular polyhedron      8 76
Ridge      85
Rule 1      2
Rule 2      6
Saddle point      85 86
Schoenfliess Theorem      95 100 103
Screwdriver rule      30
Sculpture, xi      56 85
Sketching      102
Skull      43 111
Slicing plane      90
Sphere      105
Sphere, punctured      26 27
Sphere, with g handles      27 43 54
Spiral approach      101
Star      76 96
Subtraction (of panel)      64
Surface: mathematical      95
Surface: mystery      76 96
Surface: paper      7
Surface: planar      14
Tape      2 65 96
Tests      17 64
tetrahedron      7 64
Theorem (explanation)      34
Theorems: Addition      48 57;
Theorems: Assembly      76 94 100
Theorems: Classification      61
Theorems: Five-colour      69
Theorems: Fundamental      58
Theorems: Gallic      58
Theorems: Heawood's      73
Theorems: Invariance      65 94
Theorems: Jordan Curve      95 100
Theorems: Orientability      78
Theorems: Schoenfliess      95 103
Theorems: Trading      46 54
Torus      7 73 94 106
Torus equation      12 106
Torus, double      27 107
Torus, punctured      21 37
Trading Theorem      46 54
Triangulation      67 96
Trick      51 102
Twist      10 17 41 80 81 99
Two-sided      29 30
Underpass      15 41 99
Understanding      104
Uniqueness (of plan)      60
Vertices      95 100
Volcano      82 85
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