How can 2D planes exist without thickness in real space?

[DOCMUR]

Hello

I'm a grade 12 math student at WCI and I need some help with planes.
As I understand it planes are 2D sections of grid. 2D sections of grid can't exist in real space because they have no thickness. How can anyone need to use something that has no thickness, why can we ever imagine it.

 

[fourier jr]

it's just like a line. a cube has length, width & depth. a plane has length & width, but no depth. a line only has length, no width or depth. a point doesn't have anything.

 

[mathwonk]

think of it as a thin imaginary sheet of space dividing one side of a 3 dimensional space from another.

 

[quetzalcoatl9]

think of it this way:

say i have a sphere made of metal. i want to paint the surface of that sphere, but i want to know exactly how much paint i will need. well, the amount of paint that i need will be equal to the surface area of the sphere.

notice that the surface giving me my surface area is 2D. Of course, the paint will have some thickness, but the surface area does not.

so there is a real-life situation where 2D works. on paint cans you will usually find a table showing how much paint you will need (volume) for such-and-such square feet (area).