Difference between revisions of "Geometry/Olympiad"

 
(10 intermediate revisions by the same user not shown)
Line 1: Line 1:
The following is a list of olympiad [[geometry]] topics.
+
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.
  
Synthetic geometry
+
== Topics ==
** [[Cyclic quadrilaterals]]
+
=== Synthetic geometry ===
***[[Ptolemy's Theorem]]
+
* [[Cyclic quadrilaterals]]
** [[Orthic triangle]]
+
**[[Ptolemy's theorem]]
** [[Incenter-Excenter Lemma]]
+
* [[Orthic triangle]]
** [[Directed angles]]
+
* [[Incenter/excenter lemma]]
** [[Radical Axis]]
+
* [[Directed angles]]
** [[Similar triangles]]
+
* [[Similar triangles]]
** [[Ceva's Theorem]]
+
* [[Power of a point theorem]]
** [[Menelaus' Theorem]]
+
* [[Radical axis]]
** [[Nine-point circle]]
+
* [[Ceva's theorem]]
** [[Euler line]]
+
* [[Menelaus' theorem]]
** [[Simson line]]
+
* [[Nine-point circle]]
** [[Isogonal conjugates]] and [[Isotomic conjugates]]
+
* [[Euler line]]
** [[Symmedians]]
+
* [[Simson line]]
Analytic Geometry
+
* [[Isogonal conjugates]] and [[Isotomic conjugates]]
** [[Trigonometry]]
+
* [[Symmedians]]
** [[Linear algebra]]
+
=== Analytic geometry ===
** [[Complex numbers]]
+
* [[Trigonometry]]
** [[Barycentric coordinates]]
+
* [[Cartesian geometry]]
** [[Trilinear coordinates]]
+
* [[Linear algebra]]
Transformations
+
* [[Complex numbers]]
** [[Homothety]]
+
* [[Barycentric coordinates]]
** [[Rotation]] and [[Reflection]]
+
=== Transformations ===
** [[Inversive geometry]]
+
* [[Homothety]]
** [[Projective geometry]]
+
* [[Rotation]] and [[Reflection]]
* Miscellaneous
+
* [[Inversive geometry]]
** [[Construction]]
+
* [[Projective geometry]]
** [[Locus]]
+
**[[Brocard's Theorem]]
** [[3D Geometry]]
+
**[[Pascal's Theorem]]
** [[Geometric Inequalities]]
+
* [[Spiral similarity]]
 +
=== Miscellaneous ===
 +
* [[Construction]]
 +
* [[Locus]]
 +
* [[3D Geometry]]
 +
* [[Geometric inequalities]]
 +
 
== Resources ==
 
== Resources ==
 
=== Books ===
 
=== Books ===
Line 38: Line 44:
 
* [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.
Line 47: Line 52:
  
 
== 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

Invalid username
Login to AoPS