Art School

This is a unit about building "diagram intuition": being able to take a geometry diagram (which may be good or bad) and trying to get a sense of which claims should or shouldn't be true.

Philosophy

When talking about geometry diagrams the most common piece of advice is "draw a good diagram so that when something is true, you can guess it from the diagram". However, you won't be able to draw a perfect diagram all the time, so it is more important to build your diagram intuition.

Some advice given in the handout are:

1. Constructing diagrams is nontrivial: Deciding how to construct the diagram is important. The order in which you draw the points can facilitate the problem, while drawing a different line horizontal can make the problem look completely foreign.
2. A lot of experts use Freehand diagrams: Making claims from diagrams is about experience. Because of this, expert geometers can get more from a freehand diagram than many beginners can from a perfect diagram.

Notable Problems

• IMO 2020/1: This is the first required problem in the unit, illustrating really well the importance of making observations from your diagram.
• Japan 2014/4: Another required problem in the unit. This problem brilliantly demonstrates how making a correct observation from the diagram solves half the problem.
• IMO 2013/3: A required problem and a 9 club in the D version. A strange geo, but extremely rewarding and perfectly illustrates the theme of this unit.