240 pages · 2023
Solid Geometry with MATLAB Programming
By Nita H. Shah · Falguni S. Acharya
- Published
- January 30, 2023
- Imprint
- River Publishers
- Edition
- 1st Edition
- ISBN
- 9781003360681
Overview
About this book
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.
Subjects
Engineering & Technology, Mathematics & Statistics
Inside the book
Table of contents
Select a chapter to read its abstract.
Chapter 1Plane
Pages: 44
A locus is a plane such that if any two points P and Q are on the locus then every point of the line PQ lies on the locus.
Chapter 2Straight Line
Pages: 44
A straight line may be generated by the intersection of two non-parallel planes. So, the general equation of a straight line is given by the combined equations of two planes as given by https://www.w3.org/1998/Math/MathML" display="block"> a 1 x + b 1 y + c 1 z + d 1 = 0 a n d a 2 x + b 2 y + c 2 z + d 2 = 0 ; parovided a 1 a 2 ≠ b 1 b 2 ≠ c 1 c 2 . https://www.w3.org/1999/xlink" content-type="black-white" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003360681/2a955a32-5d0d-46bc-9b74-74284dc76385/content/math3_45_1_B.tif"/>
Chapter 3Sphere
Pages: 44
The sphere is a locus of a point that moves so that its distance from a fixed point always remains constant.
Chapter 4Cone
Pages: 33
A cone is a surface generated by a straight line that passes through a fixed point and satisfies one more condition.
Chapter 5Cylinder
Pages: 17
A cylinder is a surface generated by straight lines parallel to a fixed-line and satisfying one more condition intersecting to a curve or touching a given surface.
Chapter 6Central Conicoid
Pages: 18
The locus of the general equation https://www.w3.org/1998/Math/MathML" display="block"> a x 2 + b y 2 + c z 2 + 2 f y z + 2 g z x + 2 h x y + 2 u x + 2 v y + 2 w z + d = 0 https://www.w3.org/1999/xlink" content-type="black-white" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003360681/2a955a32-5d0d-46bc-9b74-74284dc76385/content/math6_185_1_B.tif"/> of the second degree in x, y and z is called a conicoid.
Chapter Chapter 7Miscellaneous Examples using MATLAB
Pages: 24
Miscellaneous Examples using MATLAB