What is an N-gon?Date: 06/01/98 at 18:17:23 From: Missy Subject: I'm confused! Dear Dr. Math, I can't figure out the answer to this question. Consider the following pattern: In an N-gon, n-3 diagonals can be drawn from one vertex. When N = 4, to what kind of polygon does the pattern refer? I don't get the part of "n-3 diagonals." Does that mean that to find the answer, I have to subract 4 from 3? Missy Date: 06/01/98 at 19:00:04 From: Doctor Barrus Subject: Re: I'm confused! Hi, Missy! I'm going to split the statement up and try to explain each part. First: "In an N-gon, n-3 diagonals can be drawn from one vertex." I think that "N" and "n" mean the same number. What this means, then, is this: Say you have a polygon with n sides (this is called an n-gon). Now pick any vertex (corner). We're going to count how many diagonals (lines connecting two vertices that don't touch the sides of the n-gon) we can draw from that vertex. For example, let's look at a hexagon: 1_______2 / \ Now pick one of the corners (Let's suppose I / \ choose corner number 1). Draw lines connecting / \ that corner with the other corners that aren't 6\ /3 already connected to corner 1. These corners are \ / 3, 4, and 5. The lines that you've drawn are the \_______/ diagonals drawn from vertex 1. 5 4 What the statement is saying is that from any vertex, or corner, of an n-gon, you can draw n-3 diagonals (in our example, we could draw n-3 = 6-3 = 3 diagonals to corners 3, 4, and 5). To see why this is, look at this: - We have n points as the vertices. - We can't draw a line connecting a point with itself. - A point is already connected to two other points by the sides of the n-gon. So we have n - 1 - 2 = n - 3 points to connect to. Therefore, there are n - 3 diagonals. Second: "When N = 4, to what kind of polygon does the pattern refer?" This is just asking what kind of polygon has 4 sides. You'll also want to look at how many diagonals the formula says you can draw from one vertex, and check that by actually drawing the diagonals. Well, I hope this helps. Good luck! -Doctor Barrus, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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