Difference between revisions of "Geometry/Olympiad"
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− | + | 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. | |
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+ | == Topics == | ||
+ | === Synthetic geometry === | ||
+ | * [[Cyclic quadrilaterals]] | ||
+ | **[[Ptolemy's theorem]] | ||
+ | * [[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 === | ||
+ | * [[Trigonometry]] | ||
+ | * [[Cartesian geometry]] | ||
+ | * [[Linear algebra]] | ||
+ | * [[Complex numbers]] | ||
+ | * [[Barycentric coordinates]] | ||
+ | === Transformations === | ||
+ | * [[Homothety]] | ||
+ | * [[Rotation]] and [[Reflection]] | ||
+ | * [[Inversive geometry]] | ||
+ | * [[Projective geometry]] | ||
+ | **[[Brocard's Theorem]] | ||
+ | **[[Pascal's Theorem]] | ||
+ | * [[Spiral similarity]] | ||
+ | === Miscellaneous === | ||
+ | * [[Construction]] | ||
+ | * [[Locus]] | ||
+ | * [[3D Geometry]] | ||
+ | * [[Geometric inequalities]] | ||
+ | |||
== Resources == | == Resources == | ||
=== Books === | === Books === | ||
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* [http://www.amazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerdtfeger. | * [http://www.amazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerdtfeger. | ||
* [http://www.amazon.com/exec/obidos/ASIN/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe. | * [http://www.amazon.com/exec/obidos/ASIN/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe. | ||
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* [http://www.amazon.com/exec/obidos/ASIN/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]]. | * [http://www.amazon.com/exec/obidos/ASIN/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]]. | ||
See [[math books]] for additional texts. | See [[math books]] for additional texts. | ||
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== See also == | == See also == | ||
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* [[Geometry/Introduction | Introductory Geometry]] | * [[Geometry/Introduction | Introductory Geometry]] | ||
* [[Geometry/Intermediate | Intermediate Geometry]] | * [[Geometry/Intermediate | Intermediate Geometry]] |
Revision as of 16:25, 18 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.
- 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.