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 |  موضوع: كتاب Solid Geometry with MATLAB Programming الجمعة 18 نوفمبر 2022, 1:15 pm | |
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أخواني في الله
أحضرت لكم كتاب
Solid Geometry with MATLAB Programming
Nita H. Shah
Gujarat University, India
Falguni S. Acharya
Parul University, India
و المحتوى كما يلي :
Contents
Preface ix
1 Plane 1
1.1 Definition . 1
1.2 General Equation of the First Degree in x, y, z Represents
a Plane . 1
1.3 Transformation of General form to Normal Form 3
1.4 Direction Cosines of the Normal to a Plane . 4
1.5 Equation of a Plane Passing through a Given Point 5
1.6 Equation of the Plane in Intercept Form . 6
1.7 Reduction of the General Equation of the Plane to the
Intercept Form . 7
1.8 Equation of a Plane Passing through three Points 10
1.9 Equation of any Plane Parallel to a Given Plane . 15
1.10 Equation of Plane Passing through the Intersection of Two
Given Planes . 16
1.11 Equation of the Plane Passing through the Intersection . 17
1.12 Angle between Two Planes 21
1.13 Position of the Origin w.r.t. the Angle between Two Planes . 23
1.14 Two Sides of a Plane . 24
1.15 Length of the Perpendicular from a Point to a Plane . 26
1.16 Bisectors of Angles between Two Planes . 28
1.17 Pair of Planes . 31
1.18 Orthogonal Projection on a Plane . 35
1.19 Volume of a Tetrahedron . 36
Exercise 42
2 Straight Line 45
2.1 Representation of Line (Introduction) 45
2.2 Equation of a Straight Line in the Symmetrical Form 45
vvi Contents
2.3 Equation of a Straight Line Passing through Two Points . 46
2.4 Transformation from the Unsymmetrical to the Symmetrical
Form 49
2.5 Angle between a Line and a Plane 53
2.6 Point of Intersection of a Line and a Plane 54
2.7 Conditions for a Line to Lie in a Plane 55
2.8 Condition of Coplanarity of Two Straight Lines . 56
2.9 Skew Lines and the Shortest Distance between Two Lines 69
2.10 Equation of Two Skew Lines in Symmetric Form 72
2.11 Intersection of Three Planes . 80
Exercise 87
3 Sphere 89
3.1 Definition . 89
3.2 Equation of Sphere in Vector Form 89
3.3 General Equation of the Sphere 91
3.4 Equation of Sphere Whose End-Points of a Diameter
are Given . 91
3.5 Equation of a Sphere Passing through the Four Points 93
3.6 Section of the Sphere by a Plane . 105
3.7 Intersection of Two Spheres 106
3.8 Intersection of Sphere S and Line L . 115
3.9 Tangent Plane . 116
3.10 Equation of the Normal to the Sphere 117
3.11 Orthogonal Sphere 127
Exercise 129
4 Cone 133
4.1 Definition . 133
4.2 Equation of a Cone with a Conic as Guiding Curve . 133
4.3 Enveloping Cone to a Surface . 138
4.4 Equation of the Cone whose Vertex is the Origin
is Homogeneous 142
4.5 Intersection of a Line with a Cone 149
4.6 Equation of a Tangent Plane at (α, β, γ) to the Cone
with Vertex Origin 150
4.7 Conditions for Tangency . 152
4.8 Right Circular Cone 156
Exercise 164Contents vii
5 Cylinder 167
5.1 Definition . 167
5.2 Equation of the Cylinder whose Generators Intersect
the Given Conic 168
5.3 Enveloping Cylinder . 170
5.4 Right Circular Cylinder 175
Exercise 182
6 Central Conicoid 185
6.1 Definition . 185
6.2 Intersection of a Line with the Central Conicoid . 185
6.3 Tangent Lines and Tangent Plane at a Point . 186
6.4 Condition of Tangency 188
6.5 Normal to Central Conicoid 191
6.6 Plane of Contact 197
6.7 Polar Plane of a Point . 197
Exercise 201
7 Miscellaneous Examples using MATLAB 203
Index 227
About the Authors 229
Index
A
Arbitrary 2, 17, 194
Axes 4, 23, 45, 72, 104,
147, 198
C
Centroid 8, 104, 198, 199
Circumcenter 14, 15
Conditions 15, 55, 82, 152
Constant 3, 29, 42, 102, 156,
214
Coordinate 3, 13, 35, 45, 72, 104,
147, 185, 198, 215
Coordinate planes 5, 35, 43
Coordinates 3, 7, 24, 43, 73, 102,
185, 216
Coplanar 10, 13, 56, 58, 93
Cosines 2, 4, 26, 45, 76, 134,
178, 202
Cross multiplication 12, 14, 20
D
Direction cosines 2–4, 45, 53, 134,
155, 178, 200
Distance 9, 26, 44, 69, 71, 88, 105,
122, 161
E
Externally 5, 25, 125, 198
F
Fixed 8, 45, 50, 89, 132, 138, 156,
175
Fixed point 8, 45, 50, 130, 138, 156
I
Intercept 6, 7, 8, 89, 130
Intercept form 6, 7, 8
Internally 5, 24, 132, 198
Intersection 9, 16, 17, 19, 42, 45, 74,
80, 106, 156, 201
Intersects 12, 43, 115, 133, 169, 185
L
Locus 1, 39, 102, 141, 200
N
Negative 4, 25, 105, 220
Normal 2, 3, 4, 116, 191, 200, 200
Normal form 2, 3, 4, 27
O
Origin 2, 23, 89, 102, 137, 150, 178,
208
P
Parallel 3, 6, 78, 122, 167, 200
227228 Index
Passing 3, 5, 95, 124, 192
Perpendicular 2, 22, 78, 105, 122,
154, 180, 211
Perpendiculars 13, 95, 153, 164
Plane 1, 5, 67, 107, 175, 201, 204
Planes 5, 31, 83, 190, 201, 207
Points 1, 26, 98, 161
Positive 3, 23, 28
Projections 2, 35, 37, 45
Proportional 4, 41, 53, 155, 160, 202
R
Ratios 4, 6, 21, 52, 148, 153, 161, 208
Reciprocals 8
Rectangular 4, 73, 83, 140, 141
S
Straight line 2, 35, 45, 47, 56, 133,
138, 175, 183
T
Triangle 8, 14, 35, 44, 130, 176
V
Value
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