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geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.

AI overview

Geometry is a branch of mathematics that studies the properties of space, including how far apart things are, what shape they have, how big they are, and where they sit relative to each other. It's one of the oldest areas of mathematics and has been a central tool for understanding the physical world and solving practical problems throughout history.

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Image: Westerner and Arab practicing geometry 15th century manuscript.jpg

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Commons category: Geometry
Classification of Instructional Programs code: 27.0104
P8168: Hamburg-Harburg Rathaus station
hashtag: geometry
Stack Exchange tag: mathematica.stackexchange.com/tags/geometry

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~34 min read

Article

42 sections

Contents

History
Main concepts
Axioms
Spaces and subspaces
Points
Lines
Planes
Curves
Surfaces
Solids
Manifolds
Angles
Measures: length, area, and volume{{anchor|Measures}}
Metrics and measures
Congruence and similarity
Compass and straightedge constructions
Rotation and orientation
Dimension
Symmetry
Contemporary geometry
Euclidean geometry
Euclidean vectors
Differential geometry
Non-Euclidean geometry
Topology
Algebraic geometry
Complex geometry
Discrete geometry
Computational geometry
Geometric group theory
Convex geometry
Applications
Art
Architecture
Physics
Other fields of mathematics
See also
Notes
References
Sources
Further reading
External links

Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained unsolved for several centuries.