Difference between revisions of "Geometry/Olympiad"
Etmetalakret (talk | contribs) |
Etmetalakret (talk | contribs) m |
||
| Line 31: | Line 31: | ||
**[[Brocard's Theorem]] | **[[Brocard's Theorem]] | ||
**[[Pascal's Theorem]] | **[[Pascal's Theorem]] | ||
| + | * [[Spiral similarity]] | ||
=== Miscellaneous === | === Miscellaneous === | ||
* [[Construction]] | * [[Construction]] | ||
Revision as of 10:59, 11 May 2021
An olympiad level study of geometry involves familiarity with intermediate topics to a high level, a multitude of new topics, and a highly developed proof-writing ability.
Contents
Topics
Synthetic geometry
- Cyclic quadrilaterals
- Orthic triangle
- Incenter/excenter lemma
- Directed angles
- Similar triangles
- Power of a point theorem
- Radical axis
- Ceva's theorem
- Menelaus' theorem
- Nine-point circle
- Euler line
- Simson line
- Isogonal conjugates and Isotomic conjugates
- Symmedians
Analytic geometry
Transformations
Miscellaneous
Resources
Books
- Euclidean Geometry In Mathematical Olympiads by Evan Chen
- Geometry Revisited -- A classic.
- Geometry of Complex Numbers by Hans Schwerdtfeger.
- Geometry: A Comprehensive Course by Dan Pedoe.
- Non-Euclidean Geometry by H.S.M. Coxeter.
- Projective Geometry by H.S.M. Coxeter.
See math books for additional texts.
Classes
- The Olympiad Geometry class, an Olympiad level course over geometry.
- The Worldwide Online Olympiad Training (WOOT) Program -- Olympiad training in various subjects including geometry.
