### Some articles on *plane, euclidean plane, euclidean*:

Lie Sphere Geometry in The Plane - The Lie Quadric

... The Lie quadric of the

... 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

... 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

... 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)

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