# Lectures 2012 - Day 3

## Accelerators And Light Sources

#### by Boris Podobedov

## Non-Euclidean Geometry

#### by Sasha Abanov

Can the sum of angles of a triangle be bigger or smaller than 180 degrees? It turns out that the answer is yes, if you are willing to do geometry on curved surfaces. We will start our discussion with Euclid’s postulates of conventional plane geometry and then use the Poincare disk model to introduce hyperbolic geometry. We will uncover Non-Euclidian geometry behind some of Escher’s lithographs and watch beautiful coverings of a hyperbolic plane.