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{{r|Euclidean geometry}}

This generalization is obtained by extending the axioms of [[Euclidean geometry]] ...it is a translation, equivalent to a shift of origin. In the classical [[Euclidean geometry]] it is irrelevant at which points in space the geometrical objects ([[circ

{{r|Euclidean geometry}}

{{Image|Line (Euclidean geometry).png|right||Line AB (in red) through points A and B (in blue). Of course, a In [[Euclidean geometry]], a '''line''' (sometimes called, more explicitly, a '''straight line''')

{{Image|Line (Euclidean geometry).png|right||Line AB (in red) through points A and B (in blue). Of course, a In [[Euclidean geometry]], a '''line''' (sometimes called, more explicitly, a '''straight line''')

*[[Euclidean geometry]]

{{r|Euclidean geometry}}

...plagiarist, but he and Reimann invented somewhat different variants of non-Euclidean geometry approximately simultaneously. [[User:Sandy Harris|Sandy Harris]] ([[User ta

...a boundary — that for any two of its points entirely contains the [[line (Euclidean geometry)|straight line]] joining them. ...be a three-dimensional [[Euclidean space]]), and by lines we mean [[Line (Euclidean geometry)|straight lines]].''

...a boundary — that for any two of its points entirely contains the [[line (Euclidean geometry)|straight line]] joining them. ...be a three-dimensional [[Euclidean space]]), and by lines we mean [[Line (Euclidean geometry)|straight lines]].''

The 2-dimensional plane, well-known from [[Euclidean geometry|elementary Euclidean geometry]], is an example of an '''affine space'''. Remember that in elementary geom

'''Euclid's Elements''' is the oldest systematic treatise on [[Euclidean geometry]]. For more than twenty centuries the ''Elements'' was the major textbook ...nitions.) It then goes on to the formulation of the five [[postulates]] of Euclidean geometry:

...idea of space from classical to modern. For the classical approach, see [[Euclidean geometry]].</div> ...n "what is the sum of the three angles of a triangle" is meaningful in the Euclidean geometry but meaningless in the projective geometry.

A polygon, in [[Euclidean geometry]], must have at least three sides. A polygon of three sides is called a [[t

...planar [[curve]] formed by the points that lie as far from a given [[line (Euclidean geometry)|line]] (the ''directrix'') as from a given [[point (geometry)|point]] (the

In [[Euclidean geometry]], the '''Pythagorean theorem''' states that:

...ry|geometric]] themes of [[tessellation]], [[polyhedron|polyhedra]], [[non-euclidean geometry]], and [[perspective]].<ref>{{cite web|url=http://www.mathacademy.com/pr/mi

...y mathematics with arithmetics, elementary [[algebra]] and 2-dimensional [[Euclidean geometry]] (plane geometry). <ref name="kiselev"> By standard arguments of plane [[Euclidean geometry]] one can compute the numerical values of sine and cosine for a few specifi

Otherwise, the graph of the equation will be a [[line (Euclidean geometry)|line]] in the plane, hence the name "linear equation". If the coefficient

* no easy description in the language of traditional Euclidean geometry