Can Two Planes Meet at a Point Instead of a Line?

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Discussion Overview

The discussion centers on the question of whether two planes can meet at a single point instead of along a line. It explores the implications of dimensionality on the intersection of planes, with a focus on theoretical and conceptual aspects.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant asserts that two planes can only intersect in a line, not at a point, unless they are the same plane.
  • Another participant disagrees, suggesting that the dimensionality of the ambient space is crucial, stating that in 3 dimensions the first participant is correct, but in 4 dimensions and higher, planes can intersect at a point.
  • A follow-up comment reiterates the dimensionality argument and questions whether the planes discussed are linear objects or of another type.

Areas of Agreement / Disagreement

Participants express disagreement regarding the intersection of planes, with competing views based on the dimensionality of the space in which the planes exist. The discussion remains unresolved.

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Is it possible for two planes to meet in a point instead of in a line?
 
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No. The only possiblities are:
1) Do not intersect. (the planes are parallel)
2) Intersect in a line.
3) Intersect in all points. (They are actually the same plane)
 
I have to disagree with HallsofIvy. The answer depends on the dimension of the ambient space in which the planes live.

In 3 dimensions, Halls is correct.

In 4 dimensions and higher, two planes (i.e., 2-dimensional objects) can certainly intersect in a point.
 
Ben Niehoff said:
I have to disagree with HallsofIvy. The answer depends on the dimension of the ambient space in which the planes live.

In 3 dimensions, Halls is correct.

In 4 dimensions and higher, two planes (i.e., 2-dimensional objects) can certainly intersect in a point.

Are these linear objects you are talking about or some other kind?
 

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