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. | + | 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 | + | **[[Ptolemy's theorem]] |
* [[Orthic triangle]] | * [[Orthic triangle]] | ||
| − | * [[Incenter/ | + | * [[Incenter/excenter lemma]] |
* [[Directed angles]] | * [[Directed angles]] | ||
| − | |||
* [[Similar triangles]] | * [[Similar triangles]] | ||
| − | * [[Ceva's | + | * [[Power of a point theorem]] |
| − | * [[Menelaus' | + | * [[Radical axis]] |
| + | * [[Ceva's theorem]] | ||
| + | * [[Menelaus' theorem]] | ||
* [[Nine-point circle]] | * [[Nine-point circle]] | ||
* [[Euler line]] | * [[Euler line]] | ||
| Line 26: | Line 27: | ||
* [[Homothety]] | * [[Homothety]] | ||
* [[Rotation]] and [[Reflection]] | * [[Rotation]] and [[Reflection]] | ||
| − | * [[ | + | * [[Circular inversion]] |
* [[Projective geometry]] | * [[Projective geometry]] | ||
**[[Brocard's Theorem]] | **[[Brocard's Theorem]] | ||
**[[Pascal's Theorem]] | **[[Pascal's Theorem]] | ||
| + | * [[Spiral similarity]] | ||
| + | |||
=== Miscellaneous === | === Miscellaneous === | ||
* [[Construction]] | * [[Construction]] | ||
| Line 42: | Line 45: | ||
* [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/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 51: | Line 53: | ||
== See also == | == See also == | ||
| − | |||
* [[Geometry/Introduction | Introductory Geometry]] | * [[Geometry/Introduction | Introductory Geometry]] | ||
* [[Geometry/Intermediate | Intermediate Geometry]] | * [[Geometry/Intermediate | Intermediate Geometry]] | ||
Latest revision as of 09:16, 18 June 2023
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.
