2D Shapes
Angle Games
More to shape than meets the eye
A Square in a round hole

I considered as an introduction to 2D shape, angle games. Angles and shapes can be seen to be very different but angle is so important to the whole interpretation of shape.

And it is the interpretation of shape that brings out the mathematician. Most can see the difference between a regular pentagon and a square - by counting the number of sides. In terms of interpretation there is such a difference in seeing the angles.

Looking at the angles between the sides (or edges). We all know the angles in a square are all 90 degrees but it takes a mathematician to see what the angles in a regular five-sided shape are. We know they are all the same size.

Is there an easy way - maybe they all add up to 360 degrees - but why should they?

Maybe if we join the vertices (the points) together using diagonals that will help us. We soon realise that at the centre of the shape all the angles do add up to 360 degrees - but that's in the centre, not the outside. Only when we realise the regularity of the shape and the properties of isosceles triangles can we finally work out what the angles MUST be. And that is maths - beautiful.