Definition:Coordinate System/Origin

Definition

The origin of a coordinate system is the zero vector.

In the $x y$-plane, it is the point:

$O = \tuple {0, 0}$

and in general, in the Euclidean space $\R^n$:

$O = \underbrace {\tuple {0, 0, \ldots, 0} }_{\text{$n$ coordinates} }$

Thus it is the point where the axes cross over each other.

Also known as

Some sources refer to the origin as the zero point.

Some source call it the origin of coordinates.

In a polar coordinate system or a spherical coordinate system, the origin is usually referred to as the pole.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text I$. Coordinates: $1$. Coordinate Network
• 1934: D.M.Y. Sommerville: Analytical Geometry of Three Dimensions ... (previous) ... (next): Chapter $\text I$: Cartesian Coordinate-system: $1.1$. Cartesian coordinates
• 1947: William H. McCrea: Analytical Geometry of Three Dimensions (2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Coordinate System: Directions: $2$. Cartesian Coordinates
• 1958: P.J. Hilton: Differential Calculus ... (previous) ... (next): Chapter $1$: Introduction to Coordinate Geometry
• 1967: D.E. Bourne and P.C. Kendall: Vector Analysis ... (previous) ... (next): Chapter $1$: Rectangular Cartesian Coordinates and Rotation of Axes: $1.1$ Rectangular cartesian coordinates
• 1972: M.A. Akivis and V.V. Goldberg: An Introduction to Linear Algebra & Tensors (translated by Richard A. Silverman) ... (previous) ... (next): Chapter $1$: Linear Spaces: $1$. Basic Concepts
• 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Rectangular co-ordinates
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cartesian coordinate system
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): origin
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cartesian coordinate system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): origin
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Descartes
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): origin

• Weisstein, Eric W. "Origin." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Origin.html