Polygons as special curves

I've drawn a few curves here and noticed that these curves on this side belong to a family that we call polygons and these curves your don't belong to that family now why should some curves belong to this family and some not belong to belong to this family you have to follow some rules now what I want you to do is just by looking at some members of this family these curves are all members of this family these curves are all not members of this family looking at these two can you guess what those rules are so we spend a little bit of time thinking about it you would have guessed okay one of the rules could be that all these curves only have straight-line segments in them there are no bent lines like these in these so maybe that's a rule the rule is that made of made of just line segments maybe that's the rule but is that the only rule because if that's the only rule then this should be part of the family called polygons because it's only made of line segments this should be a part of this family called polygons because it has only line segments so is this okay so maybe there is there are more rules that we don't know maybe this is one rule let's keep it here what's the other rule that's possible so I look here and this is not part of the family but this is and this very small difference between the two and that is that this is open and this is closed and then I notice that okay all of these are closed which means they have an inside and an outside what we call the interior region and the exterior region so then I guess that okay the other rule that you know the members should fall of this family that they should be closed so if you are a curve you should be closed and also made of only line segments then you'd belong to this family called polygons because if it's only closed I know that a circle would be part of this family but circle is not part of the family if it's only closed and this will also be apart this will also be apart but we know these are all not part of this family called polygons so but if I take both of these closed and made of just line segments then I can see that okay this is closed made of only line segments this is closed made of only line segments so maybe these two are the only rules but then I come here I see this okay this is made of only line segments and it is close there is there is a region inside and then there is a region outside so is this this is kind of closed so what's going on this one more small rule that we need that the curve needs to be what we call simple now if you remember a simple curve is just one where if you take a corner like this you will only have two lines leaving from that you'll never have three or more we will here again if you notice there are three lines leaving from this place so it's not a simple curve but if you notice here all the all the corners have only a maximum of two lines leaving from them and in fact they'll always have two lines because you have to be closed so you look at all of them they'd only be two lines leaving in other words you'll never have two regions like this you only have one region so now I know that as long as a curve follows these three rules it can be a member of this family that we call polygons simple closed and made up of just straight line segments