Geometry

Geometry is the field of mathematics dealing with figures in a given space.

Introductory Topics

• Area
• Circles
• Similar figures
• Triangles
• Parallel lines
• Quadrilaterals
• Polygons
• Power of a point
• Triangle inequality

Intermediate Topics

• Angle bisector theorem
• Area
• Mass Point Geometry
• Ptolemy's Theorem
• Cyclic quadrilaterals
• Stewart's Theorem
• Trigonometry

Olympiad Topics

• Brocard points
• Collinearity
• Complex numbers
• Concurrency
• Directed angles
• Geometric inequalities
• Homothecy
• Inversion
• Isogonal conjugates
• Projective geometry
• Radical axis
• Transformations
• Trigonometry

Other Topics of Interest

• The notion of dimensions
  • n-space

Resouces

Listed below are various geometry resources including books, classes, websites, and computer software.

Books

• Introductory
  • Introduction to Geometry by Richard Rusczyk (details)
• Intermediate
  • Challenging Problems in Geometry by Posamentier, Salkind (details)
• Olympiad
  • Advanced Euclidean Geometry by Posamentier (details)
  • Geometry Revisited by Coxeter and Greitzer (details)
  • Geometry Unbound

Websites

All of these links are outside of [AoPSWiki].

• Cut-the-Knot's Geometry Section
• The Geometry Junkyard
• AoPS/Mathlinks Olympiad Geometry Section

Software

These are all outside links.

• Geometer
• The Geometer's Sketchpad
• KSEG

Miscellaneous

• Introductory
  • Introduction to Geometry Course (details)