Jennings G.A. — Modern Geometry with Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Jennings G.A. — Modern Geometry with Applications

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Название: Modern Geometry with Applications

Автор: Jennings G.A.

Аннотация:

This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides Special Relativity, it covers two other important ares of non-Euclidean goemetry: spherical geometry (used in navigation and astronomy) and projective geometry (used in art). In addition, it reviews many useful topics from Euclidean geometry, emphasizing transformations, and includes a chapter on conics and planetary orbits. Applications are stressed throughout the book. Every topic is motivated by an application and many additional applications are given in the exercises. The book would be an excellent introduction to higher geometry for those students, especially prospective mathematics and teachers, who need to know how geometry is used in addition to its formal theory.

Язык:

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 187

Добавлена в каталог: 16.04.2005

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Предметный указатель

$\mathbf E^n$       1
$\mathbf P^n$       120
$\mathbf R^n$       1
Addition formulas      27 181
Addition of velocity      157 166 177
Algebraic curve      140 141
Alternate interior-exterior angles      18
Altitude      35
Angle of incidence      12
Angle of reflection      12
Angle of rotation      9
Angle-side-angle      28 61
Arc angle      49
Axis of rotation      10
Brianchon's theorem      149
Center of rotation      9
Central projection      66—70 116 133—136
Circumscribed circle      34 35
Coincident lines      122
Complete quadrilateral      132
Conformal map      72—75
Congruence      3
conic      83—113
Conic, directrix      90—92
Conic, ecentricity      90
Conic, equation in polar coordinates      99
Conic, focus      86—92 96—98
Conic, projective      130
Conic, singular      84
Conic, smooth      84
Conic, tangent line      see tangent
Conic, types of      84
Cross ratio      126—131
Curved space      19
Cylindrical projection      70—73
Dandelin, G, P      86
Desargues' theorem      122 139
Directrix, see conic
dodecahedron      60
Dot product      26 169
Dual projective curve      144
Dual projective space      136
Dual spherical triangle      55—59
Eccentricity      90
Einstein's train      168
ellipse      84 87—88 93 98
Euclid      21 27
Euclidean motion      2
Euclidean space      1
Event      154
Focus      see conic
Fourth harmonic      132
Function      2
Future pointing vector      171
Galilean observer      157
Galilean spacetime      157
Galilean transformation      155—159
Generator      83
Geodesic      43—48
Geodesic triangle      44
Great circle      46 47
Hexagon      147
Homogeneous coordinates      136
Homogeneous polynomial      140
Homogenization      141
Horizon      118
Hyperbola      84 89—90 93 97 98
Hyperbolic angle      176
Hyperbolic functions      178—181
icosahedron      62
Inertial coordinates      102 155
Inertial observer      155
Inscribed circle      33
Inverse of      3 38
Isometry      2—17 36—38 170
Isosceles triangle      28
Kepler's laws      101 104—108
Kepler, Johannes      101
Law of Cosines      26 54
Law of Sines      26 34 62
Length, contraction      168

Length, of a vector in Minkowski space      172
Length, of a worldline      174—176
Lightlike vector      171
Line at infinity      117
LORAN      99
Lorentz transformation      159—165 169
Lorentz — FitzGerald contraction      167
Material particle      171
Mercator      73
Mercator projection      73—74
Minkowski geometry      169—177
Minkowski isometry      170
Minkowski observer      165
Minkowski product      169 171
Minkowski spacetime      165
Mirror      12—14 96—98
Newton's Laws      102
Orbit of planet      101—109
Orientation      1 6 37
orthocenter      35
Pappus      22
Pappus' theorem      138
parabola      84 92 94 96 98
Parallel lines      17
Parallel postulate      17
Parallel projection      116
Pascal's theorem      147 149
Perspective      119
Perspective drawing      115
Perspective, in      122
Planimeter      39—42
Point at infinity      117
Polar triangle      55
Principle of relativity      155
Projective duality      137
Projective space      120
Projectivization      117
Pseudocircle      176
Pythagorean Theorem      22—23 173
Pythagorean triple      78—80
Radial line, plane      117
Rational trigonometric function      80—82
Reflection      3—8 10 11
Right-hand rule      6 10
Rotation      9—10 17
Sector      51
Side-angle- side      55
Side-angle-side      27
Side-side-side      28 55
Similar triangles      21—22
Simultaneous events      156 159—160
Singular point      143
Spacelike vector      171 172
Spacetime      153—154
Special relativity      153—177
Spherical coordinates      47
Spherical triangle      48—66
Stereographic projection      74—82
Sum of angles      19 51
Sundial      84
Tangent to a circle      30—33
Tangent to a conic      149
Tangent to a hyperbola      93
Tangent to a parabola      94
Tangent to a smooth conic      93
Tangent to a sphere      31 33
Tangent to an ellipse      93
Time contraction      167
Time orientation      171
Timelike vector      171 172
Translation      7—10 15
triangle      122
Triangle inequality      173
Trigonometry      23 25
Twin paradox      167 174
Vanishing point      118
Vector      5 7—9
Vertex angle      49 53
Vertex half-angle      83
Vertical angles      18
Viewplane      118
Worldline      154 171

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