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.
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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.
  
 
== Topics ==
 
== Topics ==
 
=== Synthetic geometry ===
 
=== Synthetic geometry ===
 
* [[Cyclic quadrilaterals]]
 
* [[Cyclic quadrilaterals]]
**[[Ptolemy's Theorem]]
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**[[Ptolemy's theorem]]
 
* [[Orthic triangle]]
 
* [[Orthic triangle]]
* [[Incenter-Excenter Lemma]]
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* [[Incenter/excenter lemma]]
 
* [[Directed angles]]
 
* [[Directed angles]]
* [[Radical Axis]]
 
 
* [[Similar triangles]]
 
* [[Similar triangles]]
* [[Ceva's Theorem]]
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* [[Power of a point theorem]]
* [[Menelaus' Theorem]]
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* [[Radical axis]]
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* [[Ceva's theorem]]
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* [[Menelaus' theorem]]
 
* [[Nine-point circle]]
 
* [[Nine-point circle]]
 
* [[Euler line]]
 
* [[Euler line]]
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=== Analytic geometry ===
 
=== Analytic geometry ===
 
* [[Trigonometry]]
 
* [[Trigonometry]]
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* [[Cartesian geometry]]
 
* [[Linear algebra]]
 
* [[Linear algebra]]
 
* [[Complex numbers]]
 
* [[Complex numbers]]
 
* [[Barycentric coordinates]]
 
* [[Barycentric coordinates]]
* [[Trilinear coordinates]]
 
 
=== Transformations ===
 
=== Transformations ===
 
* [[Homothety]]
 
* [[Homothety]]
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**[[Brocard's Theorem]]
 
**[[Brocard's Theorem]]
 
**[[Pascal's Theorem]]
 
**[[Pascal's Theorem]]
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* [[Spiral similarity]]
 
=== Miscellaneous ===
 
=== Miscellaneous ===
 
* [[Construction]]
 
* [[Construction]]
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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.
* [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.
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== 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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