The main results of this paper are obtained for tilings in the Euclidean plane
It is well known that the infinite elements (points and line) play a crucial role in the Euclidean model of the projective space and all the sketches of the problems are made in the extended Euclidean plane
At R = [infinity] and equal coefficients (9) the elliptic sphere transforms into the Euclidean plane
and Pythagoras' theorem begins to rule again (4).
The conical curves (circle, ellipse, hyperbola, parabola) considered on the Euclidean plane
are widely known and can also be found in the navigational applications.
As we mentioned before, the notion of affine orthogonality with respect to circular discs in the Euclidean plane
coincides with the usual Euclidean orthogonality.
Finally, a completed "straight line" in the elliptic plane does not divide the plane into two parts as infinite straight lines do in the Euclidean plane
After a historical introduction, he develops analytic projective geometry as an extension of the geometry of the euclidean plane
, sets out the axiomatic foundation of it, and introduces a metric into it.
A square grid on the Euclidean plane
consists of all points (m, n), where m and n are integers.
12" is disclosed not to be the unitary object that its representation on the Cartesian, Euclidean plane
of the score suggests, but the locus of a complex of interacting perceptual frames.
A drawing of a graph G is a representation of G in the Euclidean plane
Second, he points out that the geometrical properties of spherical figures are not the properties familiar to us from Euclidean plane
Just as a flat surface--like that of a sheet of paper--is a piece of the infinite mathematical surface known as the Euclidean plane
, a saddle-shaped surface can be thought of as a small piece of the hyperbolic plane.
Besides, it seemed that in this non-Euclidean geometry the calculations to determine length and area were much more complex than on the Euclidean plane
Th Euclidean plane
is divided in two parts separated by a vertical straight line U The right-hand side of the plane is the 'inside' of the 'urn' and the left-hand side the 'outside'.
A unit disk graph is associated with a set of unit disks in the Euclidean plane