Difference between revisions of "Geometry/Olympiad"

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The following is a list of olympiad [[geometry]] topics.
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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.
  
* [[3D Geometry]]
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== Topics ==
* [[Brocard point]]
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=== Synthetic geometry ===
* [[Collinearity]]
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* [[Cyclic quadrilaterals]]
* [[Complex numbers]]
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**[[Ptolemy's theorem]]
* [[Concurrency]]
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* [[Orthic triangle]]
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* [[Incenter/excenter lemma]]
 
* [[Directed angles]]
 
* [[Directed angles]]
* [[Geometric inequalities]]
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* [[Similar triangles]]
* [[Homothecy]]
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* [[Power of a point theorem]]
* [[Inversion]]
 
* [[Isogonal conjugate]]
 
* [[Projective geometry]]
 
 
* [[Radical axis]]
 
* [[Radical axis]]
* [[Transformations]]
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* [[Ceva's theorem]]
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* [[Menelaus' theorem]]
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* [[Nine-point circle]]
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* [[Euler line]]
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* [[Simson line]]
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* [[Isogonal conjugates]] and [[Isotomic conjugates]]
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* [[Symmedians]]
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=== Analytic geometry ===
 
* [[Trigonometry]]
 
* [[Trigonometry]]
* [[Trilinear Coordinates]]
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* [[Cartesian geometry]]
 
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* [[Linear algebra]]
 
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* [[Complex numbers]]
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* [[Barycentric coordinates]]
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=== Transformations ===
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* [[Homothety]]
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* [[Rotation]] and [[Reflection]]
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* [[Inversive geometry]]
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* [[Projective geometry]]
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**[[Brocard's Theorem]]
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**[[Pascal's Theorem]]
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* [[Spiral similarity]]
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=== Miscellaneous ===
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* [[Construction]]
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* [[Locus]]
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* [[3D Geometry]]
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* [[Geometric inequalities]]
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== Resources ==
 
== Resources ==
 
=== Books ===
 
=== Books ===
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*[https://www.amazon.com/Euclidean-Geometry-Mathematical-Olympiads-Problem/dp/0883858398/ref=cm_cr_arp_d_product_top?ie=UTF8 Euclidean Geometry In Mathematical Olympiads] by [[Evan Chen]]
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic.
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic.
* [http://www.amazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerfdtfeger.
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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/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.
* [http://www.amazon.com/exec/obidos/ASIN/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]].
 
 
* [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.
  
 
=== Classes ===
 
=== Classes ===
* The [http://www.artofproblemsolving.com/school/course/olympiad-geometry Olympiad Geoemtry] class, an Olympiad level course over geometry.
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* The [http://www.artofproblemsolving.com/school/course/olympiad-geometry Olympiad Geometry] class, an Olympiad level course over geometry.
* The [http://www.artofproblemsolving.com/school/course/woot Worldwide Online Olympiad Training (WOOT) Program] -- Olympiad training in a variety of subjects, including geometry.
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* The [http://www.artofproblemsolving.com/school/course/woot Worldwide Online Olympiad Training (WOOT) Program] -- Olympiad training in various subjects including geometry.
  
 
== See also ==
 
== See also ==
* [[Geometry]]
 
 
* [[Geometry/Introduction | Introductory Geometry]]
 
* [[Geometry/Introduction | Introductory Geometry]]
 
* [[Geometry/Intermediate | Intermediate Geometry]]
 
* [[Geometry/Intermediate | Intermediate Geometry]]

Latest revision as of 16:25, 18 May 2021

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