Strip

A Strip of Paper Only

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Strip to Cube
More Paper Foldings
A Strip of Paper Only on the Internet.

To the Main Page "Mathematische Basteleien"

Zeppelin
Cut two notches into a strip of paper (e.g. 1cm x 10cm) as shown in the drawing. Bend the strip in the middle and fasten the two ends with the help of the two
notches.

The resulting shape reminds you of a Zeppelin airship. It is interesting to discover that if you drop the Zeppelin it rotates around a horizontal axis if you offer a little help as you release it.

The Zeppelin demonstrates stability in its descent because its moment of inertia is minimal. The shape causes a torque which maintains the rotation.

It is said that playing with this was very popular in the 1930's when the public's interest in airships was at its height.

Knot top
It is a surprise to discover that a pentagon appears when you tie a knot in a strip of paper.

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The knot becomes a threedimensional star, when you loosely wrap the strip around the pentagon several times, put the ends inside, and make indentations with your fingernail.

You can find the "Lucky Star"on the internet (URLs below).

Dish of a strip top
Helmut Bichler sent me a dish and its drawing, which is formed of six pentagons. It is special that it is folded of one telex strip and that the beginning and the end meet at the same place.

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You can recognize in the backlighting technique, that each pentagon has a pentagram inside.

You can interpret the dish as part of the dodecahedron.

Producing a Sound top

If you place a strip of paper (e.g. 1cm x 10cm) between the two balls of the thumbs and blow strongly into the little gap beneath, you will produce a loud, rude sound.
You can produce a similar sound if you use a wide blade of grass.

Spiral top

...... A strip of paper becomes a spiral, if you pull the strip between the thumb and the edge of a knife, pressing hard. The spiral becomes a curl where gravity is present.

You use this effect to decorate the ends of synthetic materials, such as the narrow colourful strips or ribbons used in gift-wrapping.

I suppose that you have to explain this effect in the same way as a bimetallic bar. You create a bimetallic bar by glueing together two strips, each made of a different metal. Once this bimetallic bar is heated, one metal strip expands more than the other causing the bar to bend.

The reason that the strip of paper bends is not the difference in temperature between the top and bottom side. The knife changes the structure of the surface of the paper. This side becomes 'shorter'. (Origin: Sendung mit der Maus und TH Aachen)

Incidentally, a strip of paper will bend slightly if you hold it in the heat of a candle flame.

Moebius' Strip top

If you glue both ends of a strip of paper you produce a ring, as shown on the left. If, however, you turn one end of another strip and glue the ends, the result is the so-called 'Moebius strip' on the right.
If you cut the ring on the left lengthways in the middle, then you have two rings.

Variations:

If you cut the ring in the same way, expect a surprising result!

Bill from Michigan gave my a hint:
"Did you ever cut a Moebius strip along the 1/3 line, instead of down the middle? Try it!"

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