MÖBIUS (02/03/12)

I had an interesting day yesterday. Out at the crack of dawn for a wander. I left the van with the stars twinkling but before I'd gone a mile the cloud came in and the mist came down, perhaps I should have said the clouds came down.

I moved a few miles up the road to the Church House Inn, unsurprisingly the weather didn’t improve, it changed , it got cooler. Not to worry, I got a book for my birthday, Professor Stuart’s Hoard of Mathematical Treasures. Now I had a choice to make, go to the pub and have a wet birthday or read Ian Stewart. I took the dogs for a wet walk whilst I pondered and debated the alternatives.

We returned wet and I settled for a day of fascinating little mathematical posers. I had to skim the book as some of the problems are far from small. As regular readers will know on wet days I tend towards colouring in as a means of passing time. You’ll be pleased to note that I’ve grown up by a year and have graduated to cutting out. Here is what I made. On first acquaintance it doesn't look very special, it looks better than it would have in white card! but it is only a bit of blue paper.

It provided me with several hours fun. It is a cylindrical band with a 180° twist and was invented by a clever chap called Augustus Möbius. This is where you are probably best clicking out. The Möbius Band has a surprising property. It only has one side. It has neither inside or outside unlike a cylindrical band. It does have three sides if one considers edges as sides which strictly speaking they are……I’m not being strictly here.

On with the cutting out. When one cuts it down the middle it obviously becomes twice as long but also becomes two sided with a 360° twist.

A mathematician confided

That a Möbius strip is onesided.

You’ll get quite a laugh

When you cut it in half,

For it stays in one piece when divided.

  Back to the scissors and bisecting it again we now get two interlocking rings with a 360° twist. Amazing what one can achieve with a strip of paper.

This is a simple introduction to Topography. It kept me amused on a damp birthday and also kept me away from the falling down water.

I will now get back to the book. Have a great weekend.