## August Möbius (1790 - 1868)

August Möbius spent much of his life working in the field of astronomy, although he is probably best known for his work in mathematics.

As with a remarkable number of other mathematicians, he started life studying something entirely different - in this case, law - but quickly moved on to the study of mathematics, astronomy and physics.

In 1813 he went to Göttingen, where he studied astronomy with Gauss, who at this time was the director of the Observatory, as well as the foremost mathematicians of his day. Gauss sparked his interest in mathematics, and he began working in earnest in both maths and astronomy.

Aged only 26, he was appointed an Extraordinary Professor of astronomy at the University of Leipzig, where he remained for a long time - he was eventually promoted to a Full Professorship only in 1844!

During his time there he was also Director of the Observatory in Liepzig, and wrote many important astronomical publications.

His name is honoured by three important mathematical objects - two in geometry (a particular favourite of his) the other in number theory.

Möbius will probably be best known to you for the famous ‘Möbius Strip’, which he invented in 1858. However, it was actually first described by another mathematician called Listing.

He was a pioneer in this area - called topology - although his description of the one-sided surface (the Möbius Strip) was only discovered after his death in a memoir.

The Möbius strip is a two-dimensional surface that has only one side. Most two dimensional surfaces have two sides of course.

You can easily make a Möbius strip using a long thin strip of rectangular paper (try 2 cm x 30 cm). Holding one end of the strip in each hand, twist over only one of the ends by 180 degrees, and stick the ends together.

The strip should now look like a ring shape with a single twist in it. You should be able to start at a point on one side (try using a pen) and trace it all the way around the Möbius strip back to where you started without taking your pen off the surface. Now try cutting it in half along its entire length - and again if you can.

Möbius also worked on geometric transformations, and a Möbius transformation of the plane is one that maps circles and lines into each other. It sounds weird, but in the process many deep geometric results can be deduced with little effort.

He is also known for a function he discovered - the Möbius function - which plays a central role in understanding prime numbers and the way they are distributed.