### 1. Fluidity

A Klein bottle with a disk removed, morphs into Mobius' briefs... and back. The theme here is the impossibility to define an orientation.

We don't understand mathematics, but get used to it (famous mathematician).

An explanation regarding that trilogy.A Klein bottle with a disk removed, morphs into Mobius' briefs... and back. The theme here is the impossibility to define an orientation.

A genus 2 surface, built from one single octogonal cell by identifying pieces of the boundary. Once the octogonal cell is open, we draw a trivial loop on the surface and follow the loop retracting in the octogonal cell. The theme here is a visualisation of a presentation of the fundamental group.

A Dehn twist on a torus. This is a homeomorphism which is the identity far from a simple closed curve: here the one along which the torus is cut. So, cut along the curve, give it a full turn and glue back. Any curve intersecting the curve along which we twist will be modified. The theme here is transformations of surfaces.

Indira Chatterji