Solid geometry with MATLAB programming
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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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Gistrup, Denmark
River Publishers
[2022]
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| Schriftenreihe: | River Publishers series in mathematical, statistical and computational modelling for engineering
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| Online-Zugang: | DE-573 URL des Erstveröffentlichers https://public.ebookcentral.proquest.com/choice/PublicFullRecord.aspx?p=30172489 Taylor & Francis EBSCOhost |
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Inhaltsangabe:
- 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
- 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)
- 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
- 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
- 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