Different
Dimensions

Now it's possible to look at different aspects of number,

and when it comes down to it they are all interrelated.

But the lines and angles and shapes of 2d geometry

take on a different life when projected into 3d.

So 2d mapping can have

co-ordinates and angular directions

to represent verticality,

showing not just roads but flyovers,

and not just cars on streets but aeroplanes in 3d space

illustrated on the computer screens of air traffic control.

But the language we use for 2d shapes

needs to change to describe shapes in 3d,

with their faces, edges and vertices.

And the variety of 2d shapes may be interesting,

for example the way that some very strange shapes

can fit together to tile a surface,

while for other shapes it is impossible.

But 3d shapes bring geometry into the world

to make all sorts of different structures,

and those different shapes and structures can have

quite different uses and properties.

Different structures

based on triangles or squares

will have very different strengths and rigidity,

different abilities

to handle compression and tension,

being squeezed or stretched,

qualities that engineers will use in different ways

when designing huge domes and suspension bridges,

and a thin skinned sphere can get strength from internal pressure,

as with balloons and bubbles.

And all these different structures can be seen in the creation around us,

from crystals like salt or diamond, to the patterns seen at an atomic level.

The structure of carbon bonding is what makes it so useful,

from diamonds to charcoal,

from graphene to the buckyball.

And when thinking in three dimensions

we can group things in different ways.

We can look at what is constant in 3d shapes

even when they are stretched and deformed,

looking for what otherwise different shapes might have in common,

as in the branch of maths known as topology.

And as is well known,

only topologists can't tell the difference

between a teacup and a doughnut.

The search for truth by means of the byways of mathematics

can sometimes lead to strange objects

like the mobius strip

or the klein bottle,

but that search can sometimes give a glimpse

of how shape and number can show a simple beauty

at the heart of what at first seems impossibly complex.

The double helix of DNA

may be enough to code the whole structure of a human body,

but it is God the Creator of both that brings them into life.