Origin (mathematics)

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Origin (mathematics)

In mathematics

Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, the origin of a Euclidean space

Euclidean space

Around 300 Before Christ, the Ancient Greece mathematician Euclid undertook a study of relationships among distances and angles, first in a plane and then in space....
is a special point

Point (geometry)

In geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue....
, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space. In a Cartesian coordinate system

Cartesian coordinate system

In mathematics, the Cartesian coordinate system is used to determine each Point uniquely in a Plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate or ordinate of the point....
, the origin is the point where the axes of the system intersect.

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In mathematics

Mathematics

Euclidean space

Around 300 Before Christ, the Ancient Greece mathematician Euclid undertook a study of relationships among distances and angles, first in a plane and then in space....
is a special point

Point (geometry)

Cartesian coordinate system

Euclidean geometry

Euclidean geometry is a mathematical system attributed to the Greek mathematics Euclid of Alexandria. Euclid's Elements is the earliest known systematic discussion of geometry....
, the origin may be chosen freely as any convenient point of reference.

The most common coordinate systems are two-dimensional (contained in a plane

Plane (mathematics)

In mathematics, a plane is a curvature surface. Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry....
) and three-dimensional (contained in a space

Space

Space is the boundless, three-dimensional extent in which Physical body and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physics usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime....
) systems, having two and three perpendicular

Perpendicular

In geometry, two line or plane , are considered perpendicular to each other if they form congruence adjacent angles angles . The term may be used as a noun or adjective....
axes, respectively. The origin divides each of these axes into two halves, a positive and a negative semiaxis. Points can then be located with reference to the origin by giving their numerical coordinates—that is, the positions of their projections along each axis, either in the positive or negative direction. The coordinates of the origin are always all zero, for example (0,0) in two dimensions and (0,0,0) in three.

Symmetry with respect to the origin

When a graph is symmetric with respect to the origin, it describes a graph that looks the same before and after the graph is rotated 180 degrees. Formally, a graph is symmetric with respect to the origin if it is unchanged when reflected across both the x-axis and y-axis.