Forms and loops

My Plan for the day

The sun is shining. Laundry day today. And send off the passport forms. And complete a Tax form. And drop the twins at a friend’s house (farm) for a last day of real freedom. And re-weigh and re-pack luggage. Want to get the weight down further and will sacrifice shirts for text-books (and I’m cutting down on them!). And, and, and… Energising and fun! 🙂

Last night I showed the children how to make Mobius loops, draw lines round them and cut them down the middle. They’re bright enough not to take it at face value. I don’t think I’ve had such good value out of two sheets of A4 and two pens for a long while!

I announced this to the world on Facebook and to my surprise, some people were interested. The interest turned into a “stream of consciousness” exchange which I thought I would edit into something a bit more coherent here.

“Mobius loops” are much easier to make than explain. Take an A4 sheet of paper and cut it half length-ways. Tape the 2 pieces end to end so you have a long strip. Now give one end a half twist, loop it round and tape it to the other end. You now have a twisted ring. This is a Mobius loop. Now the fun starts. Place it on the table and draw a line round the middle of ONLY THE INSIDE of the loop (like the dotted line in the middle of the road. You may be surprised by what happens! Now, take a pair of scissors and cut along the line you’ve just drawn. You may be surprised again. Now repeat the last two steps; line (if you want to), and cut (essential). You may be surprised yet again! Try it yourself. This involves weird mathematics and even has practical applications, but most important, is just fun! Has been used to entertain; small ones, teenagers (my two) and middle-aged men (me). Ever so simple. Seems like magic, even/especially when you are doing it yourself. See the picture here.
Everyone seems to find them truly amazing. Found another surprise… Try this: Make your loop. Draw the line in the middle “round the inside”. DON’T cut! Remind them, or ask them what happened last time. Now draw a second line, between the middle line and an outside edge. Get them to examine what they’ve done. Now cut around the second line. Surprise! When they’ve got over that, draw a line around the second loop and cut along that. Surprise! How did that happen? You’re right. Perfect for a wet day anywhere. All you need is paper (and not much of that), sellotape, scissors and a pen. The trick is to get “them” to do the work. To start off with, they think they are doing something wrong (especially when I say “I told you to draw the line on one side only!”). Have fun!

This is an activity for all ages. Well worth trying it out by yourself, even if you are an adult. Perfect for an evening with half and eye on the TV. They really are amazing. And so simple. The explanations are much more difficult than the actual doing. Some of the time it actually FEELs like you’re doing magic. I know what I’m doing and still don’t really understand what I get!

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