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2. You may already have a notion of what a convex region is, but here's a mathematical definition. Definition 3.2 A region R is convex if the line segment connecting any two points in R lies in R. A polygo convex if it and its interior form a convex region. A consequence of this definition is that all the diagonals of a convex polygon lie inside the polygon. U induction to prove that a convex n-gon has n(n - 3)/2 diagonals. (Hint: Think of an n-gon as having (n-1)-gon inside of it.)

2. You may already have a notion of what a convex region is, but here's a mathematical definition. Definition 3.2 A region R is convex if the line segment connecting any two points in R lies in R. A polygo convex if it and its interior form a convex region. A consequence of this definition is that all the diagonals of a convex polygon lie inside the polygon. U induction to prove that a convex n-gon has n(n - 3)/2 diagonals. (Hint: Think of an n-gon as having (n-1)-gon inside of it.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. You may already have a notion of what a convex region is, but here's a mathematical definition. Definition 3.2 A region R is convex if the line segment connecting any two points in R lies in R. A polygon convex if it and its interior form a convex region. A consequence of this definition is that all the diagonals of a convex polygon lie inside the polygon. U induction to prove that a convex n-gon has n(n-3)/2 diagonals. (Hint: Think of an n-gon as having a (n-1)-gon inside of it.) 2 Inc
Transcribed Image Text:2. You may already have a notion of what a convex region is, but here's a mathematical definition. Definition 3.2 A region R is convex if the line segment connecting any two points in R lies in R. A polygon convex if it and its interior form a convex region. A consequence of this definition is that all the diagonals of a convex polygon lie inside the polygon. U induction to prove that a convex n-gon has n(n-3)/2 diagonals. (Hint: Think of an n-gon as having a (n-1)-gon inside of it.) 2 Inc
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