Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Theorem: The number of diagonals of a regular n- Define P (n) = n(n-3) 2 gon is 2 for n ≥ 3 Use the following bullet points and the picture to help write your proof by induction. Break down method: Start with a k+1-gon. Select a vertex and remove it and the k edges attached to it. The resulting figure is a k-gon so you have P(k) diagonals. Add back the vertex and the k edges to form the k+1-gon. Determine how many of these k edges are diagonals (or how many are not diagonals). Determine if any of the edges in the k-gon are now diagonals of the k+1-gon but were not in the k-gon. Build up method: Start with a k-gon. It has P(k) diagonals. Add a new vertex and connect it to the k vertices of the k-gon so k edges are added.

Theorem: The number of diagonals of a regular n- Define P (n) = n(n-3) 2 gon is 2 for n ≥ 3 Use the following bullet points and the picture to help write your proof by induction. Break down method: Start with a k+1-gon. Select a vertex and remove it and the k edges attached to it. The resulting figure is a k-gon so you have P(k) diagonals. Add back the vertex and the k edges to form the k+1-gon. Determine how many of these k edges are diagonals (or how many are not diagonals). Determine if any of the edges in the k-gon are now diagonals of the k+1-gon but were not in the k-gon. Build up method: Start with a k-gon. It has P(k) diagonals. Add a new vertex and connect it to the k vertices of the k-gon so k edges are added.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Please write a proof by induction for the following problem

Theorem: The number of diagonals of a regular n- Define P (n) = n(n-3) 2 gon is n(n − 3) 2 - for n ≥ 3 Use the following bullet points and the picture to help write your proof by induction. Break down method: Start with a k+1-gon. Select a vertex and remove it and the k edges attached to it. The resulting figure is a k-gon so you have P(k) diagonals. Add back the vertex and the k edges to form the k+1-gon. Determine how many of these k edges are diagonals (or how many are not diagonals). Determine if any of the edges in the k-gon are now diagonals of the k+1-gon but were not in the k-gon. Build up method: Start with a k-gon. It has P(k) diagonals. Add a new vertex and connect it to the k vertices of the k-gon so k edges are added. This creates a k+1-gon. Determine how many of these k edges are diagonals of the k+1-gon (or how many are not diagonals). Determine if any of the edges in the k-gon are now diagonals of the k+1-gon but were not in the k-gon.
Transcribed Image Text:Theorem: The number of diagonals of a regular n- Define P (n) = n(n-3) 2 gon is n(n − 3) 2 - for n ≥ 3 Use the following bullet points and the picture to help write your proof by induction. Break down method: Start with a k+1-gon. Select a vertex and remove it and the k edges attached to it. The resulting figure is a k-gon so you have P(k) diagonals. Add back the vertex and the k edges to form the k+1-gon. Determine how many of these k edges are diagonals (or how many are not diagonals). Determine if any of the edges in the k-gon are now diagonals of the k+1-gon but were not in the k-gon. Build up method: Start with a k-gon. It has P(k) diagonals. Add a new vertex and connect it to the k vertices of the k-gon so k edges are added. This creates a k+1-gon. Determine how many of these k edges are diagonals of the k+1-gon (or how many are not diagonals). Determine if any of the edges in the k-gon are now diagonals of the k+1-gon but were not in the k-gon.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS