coordinates

Likewise, in a plane, an origin O is chosen (which has coordinates x = y = 0), and a first line in the plane is chosen as the x-axis, and a point on the line is assigned an x-coordinate as previously, and a zero y-coordinate. A second line, perpendicular to the first, can be constructed and each point of that line assigned a y-coordinate as previously (using the same unit length) and an x-coordinate of zero. For any point Q in the plane, let M and N be points on the x-axis and y-axis such that QM is parallel to the y-axis and QN is parallel to the x-axis. If M has coordinates (x,0) and N has coordinates (0,y) then Q is assigned coordinates (x,y).

This process can be extended to any finite-dimensional Euclidean space. Here the coordinates have been defined in such a way that the canonical basis is an orthonormal basis, but a basis can more generally be used to assign coordinates; the axes would not generally be perpendicular and standard formulae (for example, for the scalar product) would not be valid.

• one-way function
• one‐sided surface
• one‐sided test
• one‐tailed test
• one‐to‐many
• one‐to‐one
• one‐to‐one correspondence
• only if
• onto
• open ball
• open cover
• open disc
• open interval
• open mapping
• open mapping theorem
• open problem
• open set
• operation
• operational research
• operator
• opposite angles
• opposite side
• optimal
• optimality condition
• optimal strategy