Maths is the Science of Pattern

So here's the latest in the penny fractals I've been making on the wall outside my office. This one shows the development of the Koch curve through four iterations. If the thin line of pennies at the top is 1 (one) or 3/3 then the next one down is 4/3 (count the "sides" = 4 over the horizontal space =3. Each successive one is 4/3 of the previous one so the next one is 16/9 and the next one is 64/27.

There are so many interesting relationships between numerical patterns. Look at this neat relationship between the Sierpinski triangle and Pascall's triangle. If you color all the even numbers one coler and all the odd numbers another color you get a Sierpinski triangle. There's also a relationship between Fibonacci numbers and Pascall's triangle. If you add the diagonal numbers in Pascall's triangle you get the Fibonacci sequence.

Wouldn't it be wonderful if young children could learn these magical mathematical relationships in elementary school rather than learning math as a disjointed unrelated group of rules and facts. It would be much easier for them to remember their addition, multiplication and subtraction facts if they saw the relationships between them.