Solid geometry with MATLAB programming / Nita H. Shah, Falguni S. Acharya.
Solid geometry is defined as the study of the geometry of three-dimensional solid figures in Euclidean space. There are numerous techniques in solid geometry, mainly analytic geometry and methods using vectors, since they use linear equations and matrix algebra. Solid geometry is quite useful in eve...
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Full Text (via Taylor & Francis) |
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| Main Authors: | , |
| Format: | eBook |
| Language: | English |
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[Place of publication not identified] :
River Publishers,
2022.
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| Series: | River Publishers series in mathematical, statistical and computational modelling for engineering.
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| Subjects: |
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| 100 | 1 | |a Shah, Nita H., |e author. |0 http://id.loc.gov/authorities/names/no2011092559. | |
| 245 | 1 | 0 | |a Solid geometry with MATLAB programming / |c Nita H. Shah, Falguni S. Acharya. |
| 264 | 1 | |a [Place of publication not identified] : |b River Publishers, |c 2022. | |
| 300 | |a 1 online resource. | ||
| 336 | |a text |b txt |2 rdacontent. | ||
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| 490 | 1 | |a River Publishers series in mathematical, statistical and computational modelling for engineering. | |
| 505 | 0 | |a Front Cover -- Solid Geometry with MATLAB Programming -- Contents -- Preface -- 1 Plane -- 1.1 Definition -- 1.2 General Equation of the First Degree in x, y, z Represents a Plane -- 1.3 Transformation of General form to Normal Form -- 1.4 Direction Cosines of the Normal to a Plane -- 1.5 Equation of a Plane Passing through a Given Point -- 1.6 Equation of the Plane in Intercept Form -- 1.7 Reduction of the General Equation of the Plane to the Intercept Form -- 1.8 Equation of a Plane Passing through three Points -- 1.9 Equation of any Plane Parallel to a Given Plane. | |
| 505 | 8 | |a 1.10 Equation of Plane Passing through the Intersection of Two Given Planes -- 1.11 Equation of the Plane Passing through the Intersection -- 1.12 Angle between Two Planes -- 1.13 Position of the Origin w.r.t. the Angle between Two Planes -- 1.14 Two Sides of a Plane -- 1.15 Length of the Perpendicular from a Point to a Plane -- 1.16 Bisectors of Angles between Two Planes -- 1.17 Pair of Planes -- 1.18 Orthogonal Projection on a Plane -- 1.19 Volume of a Tetrahedron -- Exercise -- 2 Straight Line -- 2.1 Representation of Line (Introduction) | |
| 505 | 8 | |a 2.2 Equation of a Straight Line in the Symmetrical Form -- 2.3 Equation of a Straight Line Passing through Two Points -- 2.4 Transformation from the Unsymmetrical to the Symmetrical Form -- 2.5 Angle between a Line and a Plane -- 2.6 Point of Intersection of a Line and a Plane -- 2.7 Conditions for a Line to Lie in a Plane -- 2.8 Condition of Coplanarity of Two Straight Lines -- 2.9 Skew Lines and the Shortest Distance between Two Lines -- 2.10 Equation of Two Skew Lines in Symmetric Form -- 2.11 Intersection of Three Planes -- Exercise -- 3 Sphere -- 3.1 Definition. | |
| 505 | 8 | |a 3.2 Equation of Sphere in Vector Form -- 3.3 General Equation of the Sphere -- 3.4 Equation of Sphere Whose End-Points of a Diameter are Given -- 3.5 Equation of a Sphere Passing through the Four Points -- 3.6 Section of the Sphere by a Plane -- 3.7 Intersection of Two Spheres -- 3.8 Intersection of Sphere S and Line L -- 3.9 Tangent Plane -- 3.10 Equation of the Normal to the Sphere -- 3.11 Orthogonal Sphere -- Exercise -- 4 Cone -- 4.1 Definition -- 4.2 Equation of a Cone with a Conic as Guiding Curve -- 4.3 Enveloping Cone to a Surface. | |
| 505 | 8 | |a 4.4 Equation of the Cone whose Vertex is the Origin is Homogeneous -- 4.5 Intersection of a Line with a Cone -- 4.6 Equation of a Tangent Plane at (a, b, r) to the Cone with Vertex Origin -- 4.7 Conditions for Tangency -- 4.8 Right Circular Cone -- Exercise -- 5 Cylinder -- 5.1 Definition -- 5.2 Equation of the Cylinder whose Generators Intersect the Given Conic -- 5.3 Enveloping Cylinder -- 5.4 Right Circular Cylinder -- Exercise -- 6 Central Conicoid -- 6.1 Definition -- 6.2 Intersection of a Line with the Central Conicoid -- 6.3 Tangent Lines and Tangent Plane at a Point. | |
| 520 | |a Solid geometry is defined as the study of the geometry of three-dimensional solid figures in Euclidean space. There are numerous techniques in solid geometry, mainly analytic geometry and methods using vectors, since they use linear equations and matrix algebra. Solid geometry is quite useful in everyday life, for example, to design different signs and symbols such as octagon shape stop signs, to indicate traffic rules, to design different 3D objects like cubicles in gaming zones, innovative lifts, creative 3D interiors, and to design 3D computer graphics. Studying solid geometry helps students to improve visualization and increase logical thinking and creativity since it is applicable everywhere in day-to-day life. It builds up a foundation for advanced levels of mathematical studies. Numerous competitive exams include solid geometry since its foundation is required to study other branches like civil engineering, mechanical engineering, computer science engineering, architecture, etc. This book is designed especially for students of all levels, and can serve as a fundamental resource for advanced level studies not only in mathematics but also in various fields like engineering, interior design, architecture, etc. It includes theoretical aspects as well as numerous solved examples. The book includes numerical problems and problems of construction as well as practical problems as an application of the respective topic. A special feature of this book is that it includes solved examples using the mathematical tool MATLAB. | ||
| 630 | 0 | 0 | |a MATLAB. |0 http://id.loc.gov/authorities/names/n92036881. |
| 650 | 0 | |a Geometry, Solid. |0 http://id.loc.gov/authorities/subjects/sh85054160. | |
| 630 | 0 | 7 | |a MATLAB. |2 fast |0 (OCoLC)fst01365096. |
| 650 | 7 | |a Geometry, Solid. |2 fast |0 (OCoLC)fst00940941. | |
| 700 | 1 | |a Acharya, Falguni S., |e author. |0 http://id.loc.gov/authorities/names/n2022058220. | |
| 776 | 0 | 8 | |i Print version: |z 8770227616 |z 9788770227612 |w (OCoLC)1342491689. |
| 830 | 0 | |a River Publishers series in mathematical, statistical and computational modelling for engineering. | |
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| 880 | 0 | |6 505-00/(S |a 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 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 164 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. | |
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