In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the Minkowski sum (also known as
dilation
Dilation (or dilatation) may refer to:
Physiology or medicine
* Cervical dilation, the widening of the cervix in childbirth, miscarriage etc.
* Coronary dilation, or coronary reflex
* Dilation and curettage, the opening of the cervix and surgi ...
) of two
sets of
position vector
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point ''P'' in space in relation to an arbitrary reference origin ''O''. Usually denoted x, r, or ...
s ''A'' and ''B'' in
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidea ...
is formed by adding each vector in ''A'' to each vector in ''B'', i.e., the set
:
Analogously, the Minkowski difference (or geometric difference) is defined using the
complement operation as
:
In general
. For instance, in a one-dimensional case