For Figure (a) of Exercise 1, find the number of faces, vertices, and edges in the polyhedron. Then verify Euler’s equation for that polyhedron.
To find:
The number of faces, vertices and edges in the polyhedron and verify Euler’s equation.
Approach:
A) Polyhedron
1) A polygon is a two dimensional shape form with more than two straight lines.
2) A polyhedron is a three-dimensional solid shape.
3) Each flat surface of a polyhedron is a polygon and is called a face.
4) The line segment where two faces of a polyhedron meet is called an edge.
5) The point where three or more edges of a polyhedron meet is called a vertex.
B) Euler’s Equation
A very important relationship between the number of vertices, faces and edges of solid shapes was discovered by a Swiss mathematician Leonard Euler.
It states
Where, V=Number of vertices, F=number of faces, E=number of edges.
Calculation:
The polyhedron ABCD is a triangular pyramid, also called as a tetrahedron
Single Variable Calculus: Early Transcendentals, Volume I
Precalculus: Mathematics for Calculus (Standalone Book)
Single Variable Calculus
Finite Mathematics and Applied Calculus (MindTap Course List)
Essentials Of Statistics
Multivariable Calculus
Elementary Technical Mathematics
Understanding Basic Statistics
Applied Calculus
Calculus: Early Transcendentals
Probability and Statistics for Engineering and the Sciences
Calculus: Early Transcendental Functions
Calculus: An Applied Approach (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Finite Mathematics
Intermediate Algebra
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Mathematical Excursions (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Calculus (MindTap Course List)
Single Variable Calculus: Early Transcendentals
Calculus of a Single Variable
Elements Of Modern Algebra
Contemporary Mathematics for Business & Consumers
Trigonometry (MindTap Course List)
Finite Mathematics for the Managerial, Life, and Social Sciences
Calculus: Early Transcendental Functions (MindTap Course List)
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
STATISTICS F/BUSINESS+ECONOMICS-TEXT
College Algebra (MindTap Course List)
Mathematics For Machine Technology
Research Methods for the Behavioral Sciences (MindTap Course List)
Introduction To Statistics And Data Analysis
Research Methods for the Behavioral Sciences (MindTap Course List)
Mathematics: A Practical Odyssey
Study Guide for Stewart's Multivariable Calculus, 8th
Statistics for Business & Economics, Revised (MindTap Course List)
Calculus (MindTap Course List)