Difference between revisions of "Geometry/Olympiad"
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| − | An olympiad level study of [[geometry]] familiarity with intermediate topics to a high level, a multitude of new topics, and a highly developed proof-writing ability. | + | 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. |
== Topics == | == Topics == | ||
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**[[Ptolemy's Theorem]] | **[[Ptolemy's Theorem]] | ||
* [[Orthic triangle]] | * [[Orthic triangle]] | ||
| − | * [[Incenter | + | * [[Incenter/Excenter Lemma]] |
* [[Directed angles]] | * [[Directed angles]] | ||
* [[Radical Axis]] | * [[Radical Axis]] | ||
| Line 19: | Line 19: | ||
=== Analytic geometry === | === Analytic geometry === | ||
* [[Trigonometry]] | * [[Trigonometry]] | ||
| + | * [[Cartesian geometry]] | ||
* [[Linear algebra]] | * [[Linear algebra]] | ||
* [[Complex numbers]] | * [[Complex numbers]] | ||
* [[Barycentric coordinates]] | * [[Barycentric coordinates]] | ||
| − | |||
=== Transformations === | === Transformations === | ||
* [[Homothety]] | * [[Homothety]] | ||
Revision as of 14:49, 9 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
- Radical Axis
- Similar triangles
- 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.
