Convex Polygons
An equilateral triangle is convex, a square is convex, and a bee will always produce a natural hexagon, completely regular and convex, like the other two. So what do we mean by convex and how did we get started?
We were looking at polygons when this problem arose, and if I may quote Emily, “some had denty bits and some didn’t”. Sarah polished it up with “… well all the corners point outwards” and Claire tried to explain that what Emily meant was that the shape “… never went in on itself”. I, of course, had to muddy the waters by suggesting that it is the opposite of concave, which I think is easier to explain.
Here we have a concave pentagon. What is true for this pentagon, and every concave polygon, is that we can always find two points within the shape, labelled here A and B , such that when we join them together the line passed out of the shape and back in again.
For a convex polygon this is never possible.
After rearrranging the words a little and drawing lots of shapes most of us felt happy with this, until Jenny asked, “… how many different regular convex polygons are there?”.
We had previously looked at internal and external angles (which some of you will call interior and exterior angles) and we had established what they were and that they added up to 180°. We had also come to the conclusiong that all the external angles of a polygon had to add up to 360°, you can see this by imagining a walk around the outside of your polygon.
Having drawn a few by means of pencil, ruler and protractor we soon decided to move over to the computer (no, not the all-singing, all-dancing multimedia PC but the old trusty BBC on the other side of the room!) and with the help of ‘SPIRALS’ we started drawing.
It soon became clear that we only got convex polygons when the external angle was a factor of 360°. So how many did we find?
Year 8 & Michael Moon
