## EDT Headstart: Exploring Shape and Space

**Mon 28 - Thu 31 July 2014
Charles Carter Building, Lancaster University**

Geometry has been a major part of mathematics since the days of the Ancient Greeks. This residential summer school will explore some of the different questions arising from geometrical problems from 2000 years ago to the present day. Participants will meet concepts from university-level mathematics and experience what it is like to study mathematics though formulating problems precisely, looking at examples, generalising and applying logical argument and proof.

### Organisation

This Summer School is part of the Engineering Development Trust (EDT) Headstart scheme and applications are administered by the EDT. *The closing dates for applications to the EDT for places was 16th January 2014 and all places are now filled.*

### What is it all about?

We will explore topics including

- combinatorial geometry: e.g. the construction of the five Platonic solids (and why there can only be five!)
- topology: how might we formally capture the idea that two different-sized squares are "the same shape"? We need to ignore lengths and focus on how shapes are joined together - this is what topology does.
- discrete geometry: if we connect some rods together by some joints, when is the result rigid or flexible? This is an interesting pure mathematical problem with some very applicable answers from small scales (understanding atomic lattices and crystals) to the large ones (construction of bridges).
- fractal geometry: fractals arise when simple geometric patterns are repeated to infinity but surprisingly also occur in nature. Fractals can have dimensions that are not whole numbers!

### What will we be doing?

- Short lectures introducing problems and techniques
- Mini-projects based on the lectures
- A major group project, extending the mini-projects
- Presentation of project results to the other participants
- Experiencing university academic and social life in lecture rooms, computer labs and halls