Take a polygon with n=10 (for example). How many diagonals can you draw from one of the corners?Natasha1 said:Homework Statement
A polygon with n sides has a total of 1/p . n . (n-q) diagonals, where p and q are integers.
(i) Find the values of p and q.
Homework Equations
The Attempt at a Solution
Can someone just help me to start on this? I know that q = 3 and p = 2 but how?
No. A diagonal links the corner to one of the other non-adjacent corners. How many of these are there (still with n=10)?Natasha1 said:9
No. A corner has 2 adjacent corners, and there is no diagonal linking a corner with itself. So, still with n=10, how many diagonals are there starting in one corner?Natasha1 said:8
Yes, that is correct. A corner of a triangle has two adjacent corners, and that's it. No possibility to draw a diagonal there.Natasha1 said:If you take a triangle with 3 sides (obviously), there are no diagonals, right?
In future posts, you need to show more of an effort than this.Natasha1 said:The Attempt at a Solution
Can someone just help me to start on this? I know that q = 3 and p = 2 but how?
No. A 4 sided polygon has 2 diagonals.Natasha1 said:So a 4 sided polygon as only 1 diagonal, am I correct?
ApologiesMark44 said:In future posts, you need to show more of an effort than this.
Yes, there is. I was trying to get you there by reasoning.Natasha1 said:But apart from trial and error is there any other way I can do this?
By reasoning how many diagonals there are. It is possible, it is easy, but you have to try it.Natasha1 said:Is there anyway I can do this problem without doing it like i have, guessing what p and q are...
How can one prove it?
The formula for calculating the number of diagonals in a polygon is n(n-3)/2, where n is the number of sides of the polygon. This formula applies to all regular and irregular polygons.
No, the number of diagonals in a polygon cannot be negative. The formula for calculating the number of diagonals will always result in a positive integer, as the number of sides and the number of diagonals must be positive values.
Yes, there is a difference between a diagonal and a side of a polygon. A diagonal is a line segment that connects two non-adjacent vertices of a polygon, while a side is a line segment that connects two adjacent vertices.
No, a polygon cannot have an infinite number of diagonals. The maximum number of diagonals a polygon can have is equal to the number of sides minus three.
A regular polygon has n-3 diagonals, where n is the number of sides. For example, a regular pentagon (5 sides) has 5-3=2 diagonals, while a regular hexagon (6 sides) has 6-3=3 diagonals.