# Riemann Surfaces

## Möbius Strip

Here is a visualisation of an example of a 2-dimensional non-orientable Riemann surface: the Möbius strip. You can magnify/rotate, etc. the surface:

NB: You might have to active dynamic evaluation of the cells in order to manipulate the surface.

## Torus moduli and fractional linear transformations

In the following you can play with the equivalence of tori whose modular parameters, τ, are related by T and S transformations. If you download the notebooks and run them in Mathematica, you can play with different values for τ.

Here you can see why tori whose modular parameters, τ, are related by T transformations, τ → τ + 1, are equivalent.

Here you can see why tori whose modular parameters are related by an S transformation, τ → -1/τ, are conformally equivalent.