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1 July 2020

The Möbius strip

A symbol of unity and connectedness.

Logo EU Council Presidency

The logo of Germany’s Presidency of the Council of the European Union is a Möbius strip. This geometric shape only has a single side, although that does not appear to be the case at first sight. The Möbius strip thus symbolises unity and connectedness in Europe, despite differing interests and a high level of diversity. It doesn’t matter what side of the Möbius strip you start on, or what direction you move in, you will always meet up on the same side. The EU member states are also interconnected, in spite of all their differences, their national interests and their divergent opinions. And they move forward together along the European path.

It’s very easy to make a Möbius strip yourself. All you need is a strip of paper. Bend it into a circle and give one end a 180 degree twist before you stick the two ends together to form a ring. This deceptively simple object has some fascinating geometric properties. For example, try colouring only one side of your Möbius strip. When you get to the end you will discover that you have coloured the entire surface.

Intertwined and inseparable

There are other fascinating things you can do with your Möbius strip. Try cutting it in half lengthwise. What do you think will happen? Most people expect to end up with two separate Möbius strips. But surprisingly, you will be left with a single loop that is twice as long as the original one and has two twists in it.

If you cut the strip twice, cutting it into thirds along its length, the result is even more surprising. The strip does in fact form two loops, but they are interlocked, and one of them is a new Möbius strip. So you can never really separate a Möbius strip.

August Ferdinand Möbius – the man who gave the strip its name

The Möbius strip is named after German mathematician and astronomer August Ferdinand Möbius (1790 – 1868). He came from Pforta and did most of his work at the University of Leipzig. Geometry was his special passion. In 1858, he described the Möbius strip. Although Johann Benedict Listing (1808 – 1882), another German mathematician, also discovered the properties of the strip in the same year, it came to be known by Möbius’s name. Möbius described his discovery as “[...] a one-sided surface for which you will need twice as much paint as you initially assumed”.

Erasmus student of his time

Was Möbius a passionate European by today’s standards? Biographers paint the picture of a scientist who had strong roots in his home state of Saxony. He turned down attractive offers from far-flung universities.

But Möbius received a grant that enabled him to spend two semesters studying with his contemporary Carl Friedrich Gauß, who was already a renowned mathematician. For that he had to go to Göttingen, which in those days was a foreign country for someone from Leipzig. He was practically an Erasmus student of his time.