Patterns
&
Sequences

You know, when you keep adding numbers to each other

in a row to make a string of numbers following each other

that is called a sequence,

and you can see patterns in the numbers of the different sequences.

So in a string of boxes containing the numbers from one to ten,

if you mark every number that you can divide by two,

what are called the even numbers,

and leave the numbers that can't be divided by two,

that we call odd.

what you have is regular stripes of odd and even.

Now one and two are simple numbers, so their pattern is simple as well,

but when you look at bigger numbers you can see patterns there as well.

Think of what you can see in a ten by ten table, with the numbers from one to one hundred.

See the patterns that show when you add numbers over and over, adding threes or fours or fives.

They have their own quite different patterns.

And to use numbers in your head it's a good idea to first learn them as their patterns in tables,

starting with one to ten times one to ten.

Or the patterns that that numbers make together,

for instance the difference between the rhythm of three and six,

and three and nine,

and six and nine.

Or the patterns that can be made with numbers in a square,

like those known as magic squares.

And there are some patterns that are there but very hard to see,

like the wonderful numbers we call primes.

Primes are numbers that cannot be exactly divided up by any smaller number

apart from the number one.

You can't make them by multiplying any other numbers together.

They are the magical building blocks of numbers,

like lego blocks of numbers in mysterious shapes

that you can never quite make out of any other smaller piece.

Then there's another kind of pattern with numbers that is really useful a lot of the time,

and it's not from numbers in sequence, but is the balance of numbers on either side of an equals sign,

a balance we call an equation.

It means that the numbers on each side are the same,

so if a number is missing you can work out what it has to be.

If we put a sign that can mean any number, like ? in an equation

we can work out what that number must be.

So 1+?=2,

or 3+?=4+2.

Because we are using numbers, and numbers always work in the same way, we know that four plus two will always make six,

and three needs another three to make six,

and nothing else will do.

And this all works because with number we can have a perfect balance,

and that is how we can see the beauty of perfect balance in the creation of which we are a part.