Geometry

Geometry (from the Ancient Greek: γεωμετρία; geo- “earth”, -metron “measurement”) is the branch of mathematics whose primary subject is spatial relationships and shapes of bodies. Geometry studies spatial relationships and shapes while ignoring other properties of real bodies (density, weight, color, etc.).

Non-Euclidean geometry

Non-Euclidean geometry means, in the literal sense — all geometric…

Euclid’s postulates

A straight line segment can be drawn joining any two…

Line segment

A line segment is defined as a portion (set of…

Ray (half-line)

A ray, or half-line, is defined as the place of…

Trihexagonal tiling

In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular…

Distance

Distance is defined to be the magnitude or size of displacement between…

Position

In order to describe the motion of an object, you…

Displacement

The displacement of an object is defined as the vector…

Coordinate system

A coordinate system is a system that uses one or…

Cartesian coordinate system

The term “cartesian coordinates” (also called rectangular coordinates) is used…

Polar coordinate system

The polar coordinate system is a two-dimensional coordinate system in…

Area

The term area is used also in a more general…

Volume

Volume is the measure of space occupied by a three-dimensional…

Focus

In geometrical optics, is called focus (or image point) the…

Algebraic geometry

Traditionally, algebraic geometry was the geometry of complex number solutions…

Geometry

Geometry (from the Ancient Greek: γεωμετρία; geo- “earth”, -metron “measurement“)…

Axiom

Euclid took an abstract approach to geometry in his Elements,…

Point

Points are considered fundamental objects in Euclidean geometry. They have…

Line

The line is one of the primitive entities of geometry…

Geodesic

In differential geometry, a geodesic is a generalization of the…

Plane

A plane is a flat, two-dimensional surface that extends infinitely…

Angle

Euclid defines a plane angle as the inclination to each…

Curve

A curve is a 1-dimensional object that may be straight…

Surface

A surface is a two-dimensional object, such as a sphere…

Manifold

A manifold is a generalization of the concepts of curve…

Dimension

Where the traditional geometry allowed dimensions 1 (a line), 2…

Space (geometry)

Space is a logical conceptual form (or structure) serving as…