### Such n tuples are sometimes called points although other nomenclature may be used see below.

**Euclidean space vs cartesian space**.
It was introduced by the ancient greek mathematician euclid of alexandria and the qualifier.
Note that he did not ever use such a term himself.
In my mind i have these concepts described in the following way.
Euclidean space is flat.

If we want to specify a given point in some two dimensional plane we could overlay that plane with a grid as follows.
The cartesian coordinate system allows us to specify directions but what about direction of rotation.
A coordinate system that specifies each point uniquely in a plane like this.
Is there such thing as cartesian euclidean and gaussian coordinate system.

A coordinate system that specifies each point uniquely in a plane like this.
Edited april 4 2012 by the.
The totality of n space is commonly denoted rn although older literature uses the symbol en or actually its non doublestruck variant en.
Xyz gaussian coordinate system.

Euclidean n space sometimes called cartesian space or simply n space is the space of all n tuples of real numbers x1 x2 xn.
But there are many cartesian coordinate systems on a euclidean space.
That parallel lines never cross.
Euclid never considered spaces where this postulate did not hold so we have named this flat space euclidean space in honour of him.

However the real n space and a euclidean n space are distinct objects strictly speaking.
Euclidean space is linear.
Rotations in euclidean space.
Since euclidean space has no preferred origin or direction we need to add a coordinate system before we can assign numerical values to points and object in the space.

Cartesian space definition ordinary two or three dimensional space.
Any euclidean n space has a coordinate system where the dot product and euclidean distance have the form shown above called cartesian.
Euclidean space is the fundamental space of classical geometryoriginally it was the three dimensional space of euclidean geometry but in modern mathematics there are euclidean spaces of any nonnegative integer dimension including the three dimensional space and the euclidean plane dimension two.
Which direction of rotation do we.

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