A point is a 0-dimensional mathematical object which can be specified in -dimensional
space using an n-tuple (, ,
..., ) consisting of coordinates. In dimensions greater than or equal to two, points
are sometimes considered synonymous with vectors and so
points in n-dimensional space are sometimes called
n-vectors. Although the notion of a point is
intuitively rather clear, the mathematical machinery used to deal with points and
point-like objects can be surprisingly slippery. This difficulty was encountered
by none other than Euclid himself who, in his Elements,
gave the vague definition of a point as "that which has no part."
The basic geometric structures of higher dimensional geometry--the line, plane, space, and hyperspace--are
all built up of infinite numbers of points arranged in particular ways.
These facts lead to the mathematical pun, "without geometry, life is pointless."
The decimal point in a decimal expansion is voiced as "point" in the United States, e.g., 3.1415 is
voiced "three point one four one five," whereas a comma
is used for this purpose in continental Europe.
-dimensional
space using an n-tuple (
, 
,
..., 
) consisting of 
coordinates. In dimensions greater than or equal to two, points
are sometimes considered synonymous with vectors and so
points in n-dimensional space are sometimes called
n-vectors. Although the notion of a point is
intuitively rather clear, the mathematical machinery used to deal with points and
point-like objects can be surprisingly slippery. This difficulty was encountered
by none other than Euclid himself who, in his Elements,
gave the vague definition of a point as "that which has no part."
