Definition:Parallel (Geometry)/Planes
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Definition
Two planes are parallel if and only if, when produced indefinitely, do not intersect at any point.
In the words of Euclid:
- Parallel planes are those which do not meet.
(The Elements: Book $\text{XI}$: Definition $8$)
The contemporary interpretation of the concept of parallelism declares that a plane is parallel to itself.
Also see
- Results about parallel planes can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): parallel
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): parallel
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): parallel