Cartesian Product
The Cartesian product of two sets 
and 
(also called the
product set, set direct product, or cross product) is defined to be the set of all
points 
where 
and 
. It is denoted 
, and is
called the Cartesian product since it originated in Descartes' formulation of analytic
geometry. In the Cartesian view, points in the plane are specified by their vertical
and horizontal coordinates, with points on a line being specified by just one coordinate.
The main examples of direct products are Euclidean
three-space (
, where 
are the real
numbers), and the plane (
).
The graph product is sometimes called the Cartesian product (Vizing 1963, Clark and Suen 2000).
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area inside x^2 - 2xy + 4y^2 = 4