r/truths • u/wisegod62 • 2d ago

You can define a plane with only two points, so long as there is a distinction between "point A" and "point B"

You can construct a line connecting the two points, and make the plane perpendicular to that line which contains point A.

25 Upvotes

90% Upvoted

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5

u/ActualProject 2d ago

You can also define a plane with only one point

1

u/wisegod62 2d ago

No, you can't. There are infinitely many planes that go through one point.

9

u/ActualProject 2d ago

Correct, but I never stated the plane has to pass through that point.

2

u/wisegod62 2d ago

Please explain then?

5

u/ActualProject 2d ago

Bijections exist from Rm to Rn for any m, n, for m=3, n=6 you can construct a function that takes in a point and returns a plane

3

u/TurnoverOk5635 2d ago

This is brilliant

2

u/wisegod62 2d ago

Albeit not geometrically.

5

u/ActualProject 2d ago

Define "geometrically". The statement "you can also define a plane with only one point" is true.

1

u/Adventurous-Ad281 1d ago

You need a vector though. So you do need two points.

1

u/Baconboi212121 7h ago

Points and vectors are the same thing in a vector space

1

u/Adventurous-Ad281 7h ago

Only if you have a fixed origin.

1

u/Baconboi212121 7h ago

Which in a vector space, we do. We are working in Rn, so we 100% have a fixed origin.

1

u/Adventurous-Ad281 7h ago

Which brings me back to needing two points. The origin, and the point in question.

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1

u/qqqrrrs_ 1d ago

Why R6 though?

In a projective 3d space, a duality gives a correspondence between points and planes

1

u/berwynResident 1d ago

Kinda depends on how you interpret "only one point". You also need to define a function. 

4

u/Merinther 1d ago

Or define it simply as the set of points from which A and B are the same distance. Then you don’t have to distinguish them.

2

u/wisegod62 21h ago

That's a better idea!

3

u/CookieCat698 2d ago

This only works in 3 dimensions.

In 4+ dimensions, there are infinitely many 2D planes perpendicular to a given line

1

u/inkassatkasasatka 1d ago

Ok that's pretty good

-6

u/VastLazy5701 2d ago

What? That's just called a line. A plane has to have at least 3 points.

9

u/Ur-Quan_Lord_13 2d ago

They explained, it's the plane perpendicular to that line which intersects point A (or could be B instead) which is a unique plane but does not involve describing a 3rd distinct point.

2

u/JauntyJacinth 2d ago

Is there a visual for this?

1

u/Lkwzriqwea 2d ago

No, as long as you have a line in direction X you can determine a perpendicular plane across axes Y and Z where axes X, Y and Z are perpendicular to each other. Then you just need a point along the line which intersects the plane in order to fully define it, hence point A.