## Archive for the ‘**Math**’ Category

## Reflected Numbers – An Idea

think about this

look at **pi**, its digits go on forever

3.14159265…

each successive digit moving to the right is an inverse power of 10. you could speak it as

3 units

1 tenth

4 hundredths

1 thousandth

5 ten thousandths

(…)

Read the rest of this entry »

## Mathematics – Unity in Diversity

One of the things about math is that the more problems we look at the more we find a finite set of mathematical objects that can be generated in more than one way, observed in more than one context. These patterns recur in varying and apparently unconnected places.

Here are just a few of the “great ideas” and their specialised manifestations. Every area of maths and science displays them. Patterns that appear in separate domains, systems, phenomena and problems. I say apparently unconnected because, if anything, writing this article has made me realise how what the mystics say is so true: all is one and interconnected.

This list is of course vastly incomplete. After a while of coming up with more and more patterns you just say “right, that’s enough to make the point!” In fact I believe the one true exhaustive list of this kind is infinite. I have no idea for a proof or disproof of that ! Suggestions please.

## Journeys In Spacetime

When they removed Einstein’s brain (don’t worry it was after his death) they found the region that usually takes the role of spatial reasoning was enlarged, actually it had crowded out part of the language region.

If you want to be like Einstein I suggest you get into visualising geometry and topology of all sorts. The easiest is to visualise a perfectly flat plane, with straight and curved journeys, triangles, squares and other shapes, but once you’ve done that you can move on up to subtler and more complex manifolds, like the sphere and then the torus, which is the shape of a ring doughnut. It’s got a hole.

Let’s allow the proportions of our torus to be about the same as the doughnut. Imagine you were an ant confined to crawl on the surface of this torus. In how many directions could you set out (following a straight line), such that you would eventually return to where you started ? Read the rest of this entry »