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.
Author(s): Nita H. Shah, Falguni S. Acharya
Series: River Publishers Series in Mathematical and Engineering Sciences
Edition: 1
Publisher: River Publishers
Year: 2023
Language: English
Pages: 230
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
6.4 Condition of Tangency
6.5 Normal to Central Conicoid
6.6 Plane of Contact
6.7 Polar Plane of a Point
Exercise
7 Miscellaneous Examples using MATLAB
Index
About the Authors
Back Cover
