Euclidean Plane

Some articles on plane, euclidean plane, euclidean:

Lie Sphere Geometry in The Plane - The Lie Quadric
... The Lie quadric of the plane is defined as follows ... This is the Euclidean plane with an ideal point at infinity, which we take to be the finite points (x,y) in the plane are then represented by the points = note that v · v = 0, v · (1,0,0,0,0) = 0 and ... points x = λ(1,0,0,0,0) + v on the Lie quadric with λ = 0 correspond to points in the Euclidean plane with an ideal point at infinity ...
Banach–Tarski Paradox - The Von Neumann Paradox in The Euclidean Plane
... In the Euclidean plane, two figures that are equidecomposable with respect to the group of Euclidean motions are necessarily of the same area, therefore, a paradoxical decomposition of a square ... by John von Neumann unlike the group SO(3) of rotations in three dimensions, the group E(2) of Euclidean motions of the plane is solvable, which implies the existence ... It is clear that if one permits similarities, any two squares in the plane become equivalent even without further subdivision ...
Euclidean Plane Isometry
... In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical ... reflections (see below under classification of Euclidean plane isometries) ... The set of Euclidean plane isometries forms a group under composition the Euclidean group in two dimensions ...
Pascal's Theorem - Euclidean Variants
... natural setting for Pascal's theorem is in a projective plane since all lines meet and no exceptions need be made for parallel lines ... parallel, the theorem remains valid in the Euclidean plane ... form pairs of parallel lines and there is no Pascal line in the Euclidean plane (in this case, the line at infinity of the extended Euclidean plane is the Pascal ...
Euclidean Plane Isometry - Informal Discussion
... Informally, a Euclidean plane isometry is any way of transforming the plane without "deforming" it ... For example, suppose that the Euclidean plane is represented by a sheet of transparent plastic sitting on a desk ... a glide reflection (see below under classification of Euclidean plane isometries) ...

Famous quotes containing the word plane:

    As for the dispute about solitude and society, any comparison is impertinent. It is an idling down on the plane at the base of a mountain, instead of climbing steadily to its top.
    Henry David Thoreau (1817–1862)