can there exist 2 dimensional plane?

Question

i argued my teacher in this,
i think that a plane must need to have x,y,z components.
so there cannot exist 2-d plane i think.

Answer 1

A two-dimensional plane is a geometric tool. Space--a three-dimensional tool--is what we live in, occupying x, y, and z axes. However, within spaces, there exist an infinite number of 2-D planes that make it up.

Normally, nothing exists solely in a two-dimensional plane. All of the objects we deal with are in a three-dimensional space. But two-dimensional planes are not physical constructs; they are building blocks of space.

For example, a line can be considered to be an infinite number of points placed in exact relation to each other. Points make up lines.
A plane can be thought of as an infinite number of parallel lines, arrayed side-by-side. Lines make up a plane.
Space can be defined as an infinite number of planes, stacked on each other like pages in a book. Planes make up space.

So, while a single plane, isolated from everything else, is merely a mathematical concept, there are an infinite number of planes surrounding us all the time--we just perceive the individual planes in massive groups, as part of the three-dimensional space in which we live, much like we perceive the individual molecules of water as the wet stuff we drink.

No, that's not entirely accurate--but no metaphor is perfect.

Answer 2

To those that said a plane can be thin but not zero
and only exist in theory:-


I can cut an object by slicing along a 2-D plane
(like a loaf of bread cut in half )

Or if you argue that plane still has thickness

Take two metal blocks (cubes) and stand them on top of each other. The join is lying in a horizontal plane with no thickness

Answer 3

A plane by definition has two dimensions.

People often work two dimensionally in the xy plane. But a plane can also exist in three dimensional space.

ax + by + cz = d

is the equation of a two dimensional plane in three dimensional space.

Answer 4

A plane is a concept with just two dimension. We can easily imagine ( Einstein said "Imagination is more important than knowledge") but,yes, can not exist in practice. As Gamow points out in his "one Two Three .... infinity" a creature of the plane can not imagine the third dimension. Perhaps it can imagine a line. We find it difficult to imagine a fourth dimension ,isn't it?

If you feel a plane cannot exist then please say, even a line can not exist. A four dimensional creature will say three dimension solid can not exist. very well !

Answer 5

Yes Plane is 3D concept(Or it can be higher dimensional)

But it can be a Special Case of 2D also

To describe a plane one needs minimum 3 points. A Plane in 1 Dimension is a Line as it's projection. Plane in 2d is a Projection of any plane in 3D.

Answer 6

2 Dimensional plane cannot exist, but for practical purposes and also for the purpose of convenience we can assume the third dimension to be negligible (for example in case of lines, we can assume that the line has no thickness)..
2 dimensions do not exist in reality as every object has length, breadth, and thickness..but for convenience purposes some objects can be considered to be in 2 dimensions only.