ABOUT ME

I live in a camper van with a couple of West Highland Terriers for company.
My passion is photography but it is a work in progress.
I am always willing to share what knowledge I have and can be contacted through the comments on this post or e-mail ADRIAN
ALL IMAGES WILL ENLARGE WITH A LEFT CLICK

Friday, 2 March 2012

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.OLYMPUS DIGITAL CAMERA 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.

OLYMPUS DIGITAL CAMERA 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.

OLYMPUS DIGITAL CAMERA  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.

21 comments:

  1. interesting images Adrian.. the little simple things make images more beautiful..have a nice weekend...

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  2. If you want to combine reading a book, topography and colouring in on the computer then I'd recommend Four Colours Suffice by Robin Wilson. It's all about proving that you only need four colours to fill in any 2D map, and the first computer proof. It also covers colouring in maps on strange shapes, including a donut. It's a few years since I read it but I enjoyed it at the time.

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    1. Mark, I started out looking at the Klein Jug. Far too complicated for me. That takes six colours.

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  3. Fascinating Adrian.
    Glad you enjoyed your special day.

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  4. Hence the expression 'get knotted' - sorry, couldn't resist that.
    Fascinating subject.

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    1. Make one John and start cutting a third of the way from the edge.

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  5. Adrian, it's good to see that you're keeping your mind and fingers active now that you've reached an advanced age!!....sorry couldn't resist!

    Interesting post.

    Coincidentally I also bought that very same book (on Kindle) a couple of weeks ago!...[;o)

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    1. Trevor, He has a previous book Cabinet Of Mathematical Curiosities.

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  6. I think you deserve a drink after that..
    Have a good weekend yourself.

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  7. Belated Happy Birthday, I'm afraid I missed your Birthday Eve post (just noticed that just now in the sidebar). Those pictures make my head spin except it was spinning already since I just spent hours trying to figure out what happened to my blog labels. I see none here either but perhaps you never used them in the first place?

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  8. That's a great one,I like this sort of stuff!
    Did you treat yourself with a nice chocolate cake? Hope you did!
    Have a good week-end Adrian!

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  9. I went to the Möbius Band concert one or two years ago. They suffered very bad, must have been watching you!!!!!!!

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  10. Next birthday you will graduate to crayoning. Or, if you'd prefer, you coould do a jigsaw. Glad you enjoyed yourself an shared it with us.

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  11. Very interesting but I don't quite see about it only being one sided. I am going to have to make one for myself I think because I need to see first hand how you can cut it into two and still have only one. Now look what you've started!

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  12. I'm sure this is fascinating and probably occupied a good amount of your time. Beats watching TV.

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  13. I'm a bit late but Happy Birthday! I knew it was coming up, then totally missed it. Darn. I hope it was a good one, seemed to be.
    I'm older than you by 9 or 10 days, depending. Oh for joy..
    Happy Birthday, Adrian!

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  14. Make that by 10 or 11 days, I see your birthday was the 2nd, I think? I also love you swirly-twirly Möbius Band!

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  15. I have internet, so thank you one and all. I'll try and get a post away this afternoon.

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  16. The artist Escher had some fun with the Mobius strip, too. He had a line of ants crawling on it. Happy belated birthday, it's great that you exercised your brain to celebrate.

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  17. Belated Happy Birthday, Adrian. That band looks like a good rainy day activity. We had one of those yesterday so will save this up for the next one.

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