Angle
&
Symmetry

Now when humans started to think about describing directions

they were faced with a number of problems.

What language would you use to explain them?

How would you control a robot

to get it from one point to another?

Well, that depends on what it knows about directions and how to move.

What if it only knew how to move north south east and west?

How would you measure how far it needs to travel in any direction,

and how to avoid objects on the way.

So one place to start would be to map out the movements on a squared grid,

which means you can explain how to get from one point to another

by only using four directions.

Of course there are other kinds of grid,

like those using a circle or polygon,

but using a square grid usually makes it easier to plot a shape's movement,

as in a translation,

or showing symmetry in a shape's reflection,

or plotting points by their co-ordinates,

all ways of seeing things that can be fun as well as useful.

But what they knew about size and place, and shape and movement,

got to be much more useful as they got to be more accurate,

knowing the exact length of lines

and the exact angle between them.

They knew about right angles,

but what about the angles in-between?

What if they didn't want north or east, but wanted an angle in-between,

like north east, or a bit south of north west?

So they decided to divide a right angle into ninety smaller angles called degrees,

and with four right angles to travel full circle, their compass now had 360 degrees,

and they could describe all sorts of different angles much more accurately.

And being able to use 360 degrees made all sorts of calculations possible,

as all straight line shapes have angles at their corners,

internal and external angles,

and the internal angles of a regular polygon will always be the same,

just as the length of its lines are the same.

And the internal angles of a triangle will always add up to 180 degrees,

while those of a quadrilateral add up to 360 degrees.

And they discovered how to use formulae and equations

to make their calculations simpler,

an easy way to see and understand

and get the answer to all the examples of a certain kind of problem.

They could use formulae

to work out the height of something at a distance,

or calculate areas of different shapes,

or the volumes of different solids,

the area of fields

or the amount of materials needed for a building.

And they saw that just as flat shapes could have symmetry around a line,

solid 3D objects could also have symmetry around a flat plane,

which was useful to give balance when constructing things,

like buildings and bridges and aeroplanes.

And by knowing shapes and volumes exactly

they could plan nets to fold and shape things in all sorts of fantastic ways,

from simple cardboard boxes to complicated origami,

complicated structures from one folded sheet,

like the complexity of creation from the One Creator,

God the Maker, God the Shaper.