Electronics, Electronics components, Experiments, History, Mechanics

What is Möbius strip?

Meeting requests, this post’s subject is the Möbius strip. It is a simple structure, but interesting and inspiration source for many professionals.

What is it and where it come from?

Möbius strip is a non-orientable surface with only one side and one edge. Watch the movement of ants in an animation of M.C. Escher’s work. To make one complete turn, ants must go through twice the length of non-twisted strip.

This Roman mosaic from the 3rd century A.D. is the oldest record found until now of Möbius strip. Was found in the villa of Sentinum, currently, Sassoferrato, and today is in Glyptothek, in Munich, Germany.

Aion mosaic Glyptothek Munich
The man standing is Aion, god of time, eras and zodiac.

In 1858, two German mathematics: August Ferdinand Möbius and Johann Benedict Listing, studied this surface’s properties independent from each other.

Making a Möbius strip

To make a Möbius strip is very easy. First, pick a rectangular paper strip.

paper strip

Make a 180º twist in the strip in a way that the most distant points find each other.

mobius strip 1

Unite the sides with a tape or glue.

Mobius strip complete

What if you cut down the strip in middle? You will have a 360º twisted strip, with half of width and double of length.

Mobius strip 360 twisted

Pick a paper strip and draw a straight line at one third distance from an edge and 2/3 from another.

2nd strip with one third line

Make a Möbius strip and then cut in this line.

2nd Möbius strip

Will appear two linked strips, one longer with a smaller width and another shorter with higher width.

two strips

A 540º or 3π twisted strip will have only one side and one edge. But, if it twisted again at 720º or 4π, will have two sides again.

Some practical applications

Conveyor belts

Conveyor belts have the shape of Möbius to avoid one side have more weariness than another, increasing durability.

Möbius resistor

This electronic component has two conductive plates separated by a dielectric.

A real resistor has inductance from leads L_{lead} and capacitance between internal electrodes C_{par}.

Real resistor

In contínuos current and low frequency, these effects can be ignored, but in high frequencies, these parasitic effects influence impedance. In Möbius resistor, magnetic fields from current cancel each other, therefore this component eliminates parasitic inductance and can be used in high frequency circuits.

Recording tapes

Some recording cassette tapes were twisted 180º to have double storage capacity.

Architecture

Exist construction projects inspired in Möbius strip, like for example the Swallow Nest, art and literature center in the city of Taichung, Taiwan.

Swallows Nest
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About Pedro Ney Stroski

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