Möbius

 

Royal Observatory Göttingen - Home to Möbius's Teacher Carl Freidrich Gauss

On this day, September 26, in 1868, Augustus Ferdinand Möbius passed away.  He was a mathematician and theoretical astronomer who studied under the legendary Carl Friedrich Gauss in Göttingen, Germany.

Display at Göttingen's Museum of Mathematical Models (Möbius Band at top left)

If you’ve heard the name Möbius before, it is probably due to an object known as the Möbius Strip or Möbius Band. Here is the item as displayed at the Museum of Mathematical Models at the Mathematical Institute of Göttingen.

A Möbius Band at Göttingen's Museum of Mathematical Models

If you’ve heard of the Möbius Band before, you know its special properties. If not, you may want to make one and explore for yourself. To make a Möbius Band, follow the directions below.

STEP 1: Take a strip of paper and give it a single twist.

Möbius Band - Step 1

STEP 2: Tape the ends together. 

Möbius Band - Step 2a

Möbius Band - Step 2b

You can stop here and admire your museum-worthy work of art, OR you can move on to:

STEP 3: Explore a property of this band by cutting it lengthwise down its middle, all the way around until you come back to where you started. If you’ve never done this before, I think you’ll be surprised with the outcome.

Möbius Band - Step 3a

Möbius Band - Step 3b (Cut all the way to where you started!)

The Möbius Strip shows up in many places outside mathematics. In literature, we find it in Howard Nemerov's poem Creation Myth on a Möbius Band; we also find it in short stories such as Martin Gardner’s No-Sided Professor, Armin Deutsch’s A Subway Named Möbius, and Arthur C. Clarke’s The Wall of Darkness. Many pieces by artist M. C. Escher make use of this shape, and the symmetry in the score of Bach’s Goldberg Variations can be thought of as having been written on a Möbius Strip.

Thanks to the mathematical mind of Augustus Ferdinand Möbius for developing this interesting object whose influence still twists through culture today.