Analytical quadrics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Pergamon Press
1960
|
| Schriftenreihe: | International series of monographs on pure and applied mathematics
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 134 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Analytical quadrics |c by Barry Spain |
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| 300 | |a IX, 134 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of monographs on pure and applied mathematics |v 14 | |
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Datensatz im Suchindex
| _version_ | 1804120000503480320 |
|---|---|
| adam_text | CONTENTS
I. INTRODUCTION
PiGE
1. Point coordinates 1
2. Distance between two points 2
3. Joachimsthal s section formula 3
4. Direction cosines 4
5. Direction ratios 5
6. Angle between two straight lines 5
7. Projections 7
II. PLANE—STRAIGHT LINE
8. Equation of a plane 9
9. Equations of a straight line 10
10. Straight line and plane 12
11. Sign of the expression u = hx + nyJrvz + p 13
12. Distance from a point to a plane 14
13. Pair of planes 15
14. Bundle of planes 15
15. Shortest distance between two skew lines 16
16. Coplanar lines 17
17. Rectangular axes related to two skew lines 18
III. SPHERE
18. Equation of sphere 20
19. Conjugate points 21
20. Pole and polar 23
21. Tangent plane and normal line 23
22. Angle of intersection of two spheres 25
23. Radical plane 25
24. Coaxal spheres 26
IV. QTJADRIC CONE—CYLINDER
25. Quadric cone 29
26. Cone with vertex at the origin 29
27. Circular cone 30
28. Conditions that y (x,y,z) be a circular cone 31
29. Angle between two generators 31
30. Reciprocal cone 33
31. Rectangular and orthogonal cones 34
32. Quadric cylinder 34
V. CENTRAL QUADRIC
33. Central quadric 36
34. Ellipsoid 37
35. Hyperboloid of one sheet 38
36. Hyperboloid of two sheets 39
37. Polar properties 39
38. Generators 41
vii
viii contents
PAGE
39. Generators of hyperboloid of one sheet 42
40. Normals 43
41. Centre of a section 44
42. Axes of central plane section 45
43. Axes of non central plane section 46
VI. PARABOLOID
44. Paraboloid 48
45. Polar properties 50
46. Generators 50
47. Generators of hyperbolic paraboloid 51
48. Normals 52
49. Centre of a section 52
50. Axes of plane section 53
VII. HOMOGENEOUS COORDINATES
51. Homogeneous coordinates 55
52. Point at infinity 55
53. Straight line 55
54. Plane 57
55. Intersection of three planes 58
56. Circle at infinity 59
57. Circular sections of central quadric 61
58. Paraboloid 62
VIII. GENERAL QUADRIC
59. Quadric 65
60. Cofactor notation 66
61. Conjugate points 66
62. Pole and polar 67
63. Tangent plane 68
64. Enveloping cone 68
65. Generators 69
66. Polar of a line 70
67. Conjugate lines 71
68. Conjugate diameters 71
69. Principal diametral planes 73
70. Discriminating cubic 74
71. Circular sections 75
72. Rank of matrix A , 76
IX. TRANSFORMATION OF AXES—INVARIANTS
73. Translation of axes 78
74. Invariants of a quadratic form under translation 79
75. Rotation of axes 80
76. Invariants of quadratic form under rotation 82
77. General transformation of coordinates 83
X. CLASSIFICATION AND REDUCTION OF QUADRIC
78. Equation of quadric 84
79. Classification of quadrics 85
80. Central quadric and cone 87
CONTENTS ix
PAGE
81. Paraboloid 88
82. Elliptic and hyperbolic cylinder 89
83. Parabolic cylinder and parallel plane pair 90
XI. FOCI—CONFOCALS
84. Focus 93
85. Foci of central quadric 94
86. Foci of paraboloid 96
87. Confocal central quadrics 97
88. Confocal paraboloids 98
XII. LINEAR SYSTEMS OF QUADRICS
89. Pencil of quadrics 101
90. Self polar tetrahedron of a pencil of quadrics 102
91. Contact of quadrics 103
92. Associated points 104
XIII. PLANE COORDINATES
93. Plane coordinates 106
94. Principle of duality 106
95. Quadric envelope 107
96. Conic 108
97. Cone 110
98. Joachimsthal s quadratic equation 110
99. Range of quadrics 112
100. Confocal quadrics 112
APPENDICES
I. Matrices 115
II. Solutions II7
INDEX 135
|
| any_adam_object | 1 |
| author | Spain, Barry |
| author_facet | Spain, Barry |
| author_role | aut |
| author_sort | Spain, Barry |
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| ctrlnum | (OCoLC)10422249 (DE-599)BVBBV005814416 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV005814416 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:35:08Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003635603 |
| oclc_num | 10422249 |
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| owner_facet | DE-703 DE-91 DE-BY-TUM DE-29T DE-83 DE-188 |
| physical | IX, 134 S. graph. Darst. |
| publishDate | 1960 |
| publishDateSearch | 1960 |
| publishDateSort | 1960 |
| publisher | Pergamon Press |
| record_format | marc |
| series | International series of monographs on pure and applied mathematics |
| series2 | International series of monographs on pure and applied mathematics |
| spelling | Spain, Barry Verfasser aut Analytical quadrics by Barry Spain New York [u.a.] Pergamon Press 1960 IX, 134 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on pure and applied mathematics 14 Quadrics Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Analytische Geometrie (DE-588)4001867-2 s DE-604 International series of monographs on pure and applied mathematics 14 (DE-604)BV001888024 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003635603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spain, Barry Analytical quadrics International series of monographs on pure and applied mathematics Quadrics Analytische Geometrie (DE-588)4001867-2 gnd |
| subject_GND | (DE-588)4001867-2 (DE-588)4151278-9 |
| title | Analytical quadrics |
| title_auth | Analytical quadrics |
| title_exact_search | Analytical quadrics |
| title_full | Analytical quadrics by Barry Spain |
| title_fullStr | Analytical quadrics by Barry Spain |
| title_full_unstemmed | Analytical quadrics by Barry Spain |
| title_short | Analytical quadrics |
| title_sort | analytical quadrics |
| topic | Quadrics Analytische Geometrie (DE-588)4001867-2 gnd |
| topic_facet | Quadrics Analytische Geometrie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003635603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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