Saturday, March 9, 2002
M I N D  G A M E S


A teasing strip on Valentine’s Day

NOW, I should have written it for Valentine’s Day, if the idea had struck me then, but for those of you who believe everyday to be a St Valentine’s Day, I have a little surprise that you can surprise your beloved with. It is so secret that even my wife does not know about it, so, I give no picture here to preserve the element of surprise.

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere. — W.S. Anglin

If you’ve never come across a Möbius Strip before, I would like to tell you that it is a looped strip with only one side and only one edge. You can make it easily yourself; just take a strip of paper, give it one twist, and join the two ends. This simple procedure gets rid of one side and one edge of your paper, even after beginning with the usual number of sides and edges — two.

To see that the Möbius Strip has only one side, try to paint it. Choose a point on the strip, begin colouring it in in one direction and you’ll find that it only has one edge. Run a pen along an edge and keep going. Since it has no reverse side, a Möbius Strip would make a good conveyor belt? The Goodrich Tyre Company has the patent on Möbius Strip belts, though the belts are not manufactured this way anymore, because the modern belt is made of an untwisted loop, with several layers of various materials.

 


Now, imagine this: On the next Valentine’s Day, you run short of ideas on what to give your beloved as a gift, you have already exhausted your allowance (or salary) or you want an extraordinary gift with a personal touch that would melt his or her heart even if it is made of stone.

In these tough conditions, try this: Make two Möbius Strips, with one twisted clockwise and the other twisted anticlockwise (If you don’t get this right, it won’t work). Stick the two loops together, at right angles to each other. Send this to the one you love, with instructions to cut along the middle of both loops. When you get to the joint, cut through both loops… and have a happy mathematical Vaaaaalentiiiine’s Daaaaaaaaaay. Just to make you feel a little less anxious, I will tell you what you will get here if you do it right — two beautiful interlocked hearts…but do these have a reverse side?

When I showed it to my friend a little while ago, he ran all the way to the house of his secret love and proposed. His girl’s father has a double-barrel gun… I hope he has a bad aim. Now, do anything, but don’t tell any Shiv Sainik about it, or you won’t get to read this column again. With this Valentine’s Day gift, we have reached a signpost, where (next week) all of you who have flooded me with letters and e-mails will get to see their names along with discussions on solutions (for some weeks to come). Do write in to me if a problem or the column has given you some trouble or sleepless nights — I’ll make it worse for you. Write at The Tribune or adityarishi99@yahoo.co.in.