A circle is a simple shape in Euclidean geometry.

Before hyperbolic geometry, mathematicians knew about two kinds of space Euclidean space, and spherical space.

In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.

Often curves in two dimensional (plane curves) or three dimensional (space curves) Euclidean space are of interest.

Moreover, the cube's being the only regular solid that tesselates Euclidean space was believed to cause the solidity of the Earth.

When n 2, the set of all such locations is called two dimensional space or bi dimensional space, and usually is thought of as a Euclidean space.

deiknymi) , or thought experiment, was the most ancient pattern of mathematical proof , and existed before Euclidean mathematics, where the emphasis was on the conceptual, rather than on the experimental part of a thought experiment.

Moreover, it has the same number of points as a square of area 1, as a cube of volume 1, and even as an unbounded n dimensional Euclidean space formula_2 (see Space filling curve).

Named for the type of zoning code adopted in the town of Euclid, Ohio, and approved in a landmark decision of the U.S. Supreme Court, Village of Euclid, Ohio v. Ambler Realty Co. Euclidean zoning codes are the most prevalent in the United States.

The scalar product also allows one to define an angle between two vectors formula_30In formula_31 dimensional Euclidean space, the standard scalar product (called the dot product) is given by formula_32 Cross product in 3 dimensional space The cross product of two vectors in 3 dimensions is a vector perpendicular to the two factors, with length equal to the area of the parallelogram spanned by the two factors.