upphafspunkti

Upphafspunkti is the term used in Icelandic mathematics to denote the origin of a coordinate system, or the baseline reference point for a vector space. It is the point from which all coordinates are measured and corresponds to the zero vector in the associated vector structure. In two-dimensional Cartesian geometry, upphafspunkti is the intersection of the x- and y-axes, with coordinates (0,0). In three dimensions it is (0,0,0). More generally, it is the unique point O such that every position vector v from O to a point P satisfies P = O + v, with O represented by the zero vector. The origin thus acts as an additive identity in the vector space of displacements.

In affine spaces, an upphafspunkti is not intrinsic to the space itself; specifying a coordinate system requires choosing an origin and an orientation, so different conventions provide different origins for the same physical space. In non-Cartesian coordinate systems, the same point can have different coordinate representations; for example, in polar coordinates the origin is the point where r = 0.

The concept is fundamental in mathematics, physics, and engineering because it provides a reference frame for measuring position, distance, and direction, and underpins linear operations, transformations, and calculations of magnitude and angle.