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. | |
| − | + | == Topics == | |
| − | + | === Synthetic geometry === | |
| − | + | * [[Cyclic quadrilaterals]] | |
| − | + | **[[Ptolemy's Theorem]] | |
| − | + | * [[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 ==== | |
| − | + | * [[Trigonometry]] | |
| − | + | * [[Linear algebra]] | |
| − | + | * [[Complex numbers]] | |
| − | + | * [[Barycentric coordinates]] | |
| − | + | * [[Trilinear coordinates]] | |
| − | + | === Transformations === | |
| − | + | * [[Homothety]] | |
| − | + | * [[Rotation]] and [[Reflection]] | |
| − | + | * [[Inversive geometry]] | |
| − | * | + | * [[Projective geometry]] |
| − | + | **[[Brocard's Theorem]] | |
| − | + | **[[Pascal's Theorem]] | |
| − | + | === Miscellaneous === | |
| − | + | * [[Construction]] | |
| + | * [[Locus]] | ||
| + | * [[3D Geometry]] | ||
| + | * [[Geometric inequalities]] | ||
| + | |||
== Resources == | == Resources == | ||
=== Books === | === Books === | ||
Revision as of 16:37, 8 May 2021
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.
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.
