## 21 April 2018

### Möbius

The Möbius strip is a surface that has only one side and only one boundary component. It has the mathematical property of being non-orientable. The Moebius strip was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in $1858$.

A model can easily be created: cutting a strip, making it a half-twist and glue up the ends, giving its characteristic shape.

The Möbius strip has several curious properties. Cutting the strip in half longitudinally of this will appear another strip (it is not a Möbius strip because it has two sides) but with twice the length of the original. Cutting the strip longitudinally about a third of their width, we obtain two strips engaged, one smaller than the other. The smallest is a Möbius strip and the biggest is not.

The Möbius strip has many applications, especially in architecture, design and engineering.

$\left(-0.99\left(x\left(x^2+y^2-z^2+1\right)-2yz\right)-2.03\left(x^2+y^2\right)\right)^2=\left(x^2+y^2\right)\left(1.01\left(x^2+y^2+z^2+1\right)-1.98\left(yz-x\right)\right)^2$