Angle
&
Symmetry

So what do we know about angles?

We know that they are the measure of how much turn a line takes in a circle around a point.

So imagine you are standing in a big circle,

like a giant clock or compass,

standing in the middle looking straight out.

Then if you are facing in a straight line looking north, on your right hand you have east,

straight behind you is south,

and to your left is west.

Now if you turn from north to east, you are turning through what is called a right angle.

And if you keep turning through another right angle you will end up facing south

Keep turning from south to west and that adds another right angle,

and turn for one more and you are back facing north where you started.

That's four right angles to turn a full circle.

So that would be the same if you moved the hand of a clock, from straight up turning it through a right angle to the number three,

another one to reach six,

another one to get to nine,

and a final right angle to get back to the number twelve at the top again.

Four right angles to go all the way round.

When we want to show there is a right angle between two lines, we mark it with a little square, to show it's that special angle,

and if we want to mark any other angles, we do it with a curve.

And because there are so many other angles that aren't right angles, we put them in different groups

and give the kind of angle in each group a name.

So angles less than a right angle are called acute angles,

those between one and two right angles are called obtuse angles,

and those bigger than two right angles are called reflex angles.

And that's an awful lot of angles.

But in the same way that you can turn a line around a point, you can turn a shape around a point,

and some shapes can rotate around a point and after turning through a certain angle they look the same as they started,

and and some shapes will look the same when they are turned through various different angles.

And some shapes have sides that mirror each other, and they call that property symmetry.

You can see symmetry when you put a mirror on a shape and look at the part of the shape that you can see along with it's reflection.

It's like you have flipped one side over.

If you can draw a line through a shape, and each side is like a reflection of the other, that is called a line of symmetry,

and some shapes can have more than one line of symmetry.

And symmetry doesn't have to be shapes with straight lines.

You can draw a wiggly line on a piece of tracing paper,

then fold the paper over and trace it to end up with a very strange symmetrical shape.

Or you can fold up a strip of paper and cut bits out of it

so when you open it you have a paper chain of symmetrical shapes.

Playing with symmetry can be great fun,

and humans tend to find symmetrical shapes beautiful,

which is perhaps because humans have a shape with a line of symmetry down their middles themselves.

You can see beauty in symmetry in all sorts of places,

and the more you learn about symmetry, the more magical it gets.