One of my all time favourite mathematical creators is the German mathematician and astronomer August Ferdinand Mobius. He was born on 17 November and died on 26 September 1868. He is world famous now for discovering the Mobius strip, a surface with only one side or boundary. It was also discovered independently by Johann Benedict Listing about the same time in 1858.
All you need to do is cut a strip of paper, twist this once then glue the ends together. What happens if you then cut this twisted strip into two with a pair of scissore, cutting along the middle, parallel to the “sides”? Imagine using Spatial Visualisation first before you actually try it.
What happens if you put two twists into your strip before you glue the ends together? Can you predict what the result will be when you use your scissors to cut along the middle of this twisted strip?
There are many Mobius Strip sculptures all over the world. We humans are intrigued by all things magical. For example, the Mobius Strip is used as a symbol of the never ending journey of goods traded from China to Venice along the Grand Silk Road. Here it is at the start of the Silk Road, at Tang West Markets in Xian.
How incredible that this objects appears to have two surfaces and two sides yet when you trace your finger along one side you quickly discover that you are back to where you started. And the same with what looks like two surfaces. Trace your finger along teh top surface and you end up at the starting point but on the underneath surface!.