Harmonic
Your friendly projective geometry unit. Harmonic bundles, poles and polars, and so on. A follow-up to Chapter 9 of EGMO.
Harmonic is a geometry unit about cross ratios and harmonic bundles.
It's considered one of the more accessible D-level units, since even though it requires some reading, the problems themselves fit pretty neatly into the theoretical framework. Its relative beginner-friendliness makes it an ideal unit to begin the year with, and for this reason it's the first unit in the OTIS ordering (excluding the Dummy Unit).
Notable problems
Most of the problems in both units (DGW and DGX) -- especially version W -- are especially clean, because they incorporate almost purely only projective geometry. Notable examples of problems include
- Taiwan Quiz 2015/3J/6: One of Evan's own creations (and also the problem featured on his homepage). Combines many incenter lemmas that were explored in the previous problems into a "grand finale", per se. A required 9 pointer on version W.
- TSTST 2015/2: An iconic problem featuring the use of special points in a triangle.
- TSTST 2019/9: a required 9 pointer on Version X, this problem is known for being ridiculously difficult for a "beginner-friendly" unit. It also features one of the rare applications of using the definition of a pencil of lines in a problem.
- Shortlist 2005 G6: A classic problem involving incircle configurations in the W version.
- Shortlist 2009 G4: Perhaps the most iconic and notable complete quadrilateral problem, present in Version X.
- Z79810E7: A lemma that is a required problem in both versions. Evan found an error in the problem that was undiscovered for 7 years.