# Difference between revisions of "Geometry/Olympiad"

Etmetalakret (talk | contribs) |
Etmetalakret (talk | contribs) |
||

(10 intermediate revisions by the same user not shown) | |||

Line 1: | Line 1: | ||

− | + | 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 == | |

− | + | === 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]] | |

− | ** [[Linear algebra]] | + | === 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 === | ||

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/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/Introduction | Introductory Geometry]] | * [[Geometry/Introduction | Introductory Geometry]] | ||

* [[Geometry/Intermediate | Intermediate Geometry]] | * [[Geometry/Intermediate | Intermediate Geometry]] |

## Latest 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.