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Intersecting, parallel and ultra parallel lines through a with respect to l in the hyperbolic plane. The parallel lines appear to intersect l just off the image. This is just an artifact of the visualisation. On a real hyperbolic plane the lines will get closer to each other and 'meet' in infinity.
Parallel play is a form of play in which children play adjacent to each other, but do not try to influence one another's behavior; it typically begins around 24–30 months. [ 1 ] [ 2 ] It is one of Parten's stages of play , following onlooker play and preceding associative play.
Parallel (latitude), an imaginary east–west line circling a globe; Parallel of declination, used in astronomy; Parallel, a geometric term of location meaning "in the same direction" Parallel electrical circuits
For an ellipse, two diameters are said to be conjugate if and only if the tangent line to the ellipse at an endpoint of one diameter is parallel to the other diameter. Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram , sometimes called a bounding parallelogram, formed by the tangent lines to the ellipse ...
In this case, one gets a parallel curve on the opposite side of the curve (see diagram on the parallel curves of a circle). One can easily check that a parallel curve of a line is a parallel line in the common sense, and the parallel curve of a circle is a concentric circle.
Two lines are parallel if and only if the two angles of any pair of consecutive interior angles of any transversal are supplementary (sum to 180°). Proposition 1.28 of Euclid's Elements , a theorem of absolute geometry (hence valid in both hyperbolic and Euclidean Geometry ), proves that if the angles of a pair of consecutive interior angles ...
Though these terms themselves may be somewhat ambiguous, they are usually used in a context in which their meaning is clear. For example, when referring to a drive shaft it is clear what is meant by axial or radial directions. Or, in a free body diagram, one may similarly infer a sense of orientation by the forces or other vectors represented.
As affine geometry deals with parallel lines, one of the properties of parallels noted by Pappus of Alexandria has been taken as a premise: [9] [10] Suppose A, B, C are on one line and A', B', C' on another. If the lines AB' and A'B are parallel and the lines BC' and B'C are parallel, then the lines CA' and C'A are parallel.