How many squares make up a cube?

Answer 1

Some would say 6.

I say the answer is 2...

A square is infinitely thin, consisting of only two dimensions: length and width.

Also, in the 2nd dimension, squares cannot overlap. They cannot exist in the same space.

If you could raise one square an infinitely small amount above another and hide the other. Then you can only see one whole square at a time, turning the object over once, you see the other one.

Measuring the depth of this object, it is clearly twice as deep as an infinitely thin square. This actual depth of two infinitesimally small sheets is unfathomable compared to any other arbitrary depth you choose to consider.

Look at the square again, from above; recall the measurement of your depth. Now, cut the side lengths of both squares down until they match the depth.

This creates a solid 3 dimensional cube, of some 3 near-infinitely small dimensions.

(QED)

What you have are these infinitely thin squares stacked to create a cube. There is no space intended between the squares.

The number of squares, in a larger cube, is directly proportional to the depth of that cube. You can only discuss each cube in relation to another cube, not to the infinitely small cubes. In other words you do not know how many sheets are used to make a 4x4x4 inch cube... per se, but you do know it is twice as many as it takes to create a 2x2x2 inch cube.

The same logic could be applied to the square itself, which is created by lines, which are themselves created by singularities (points) which each utterly fill their 0th dimension. So when we measure anything, it is only relative to some arbitrary size we have chosen to call a 1, and not infinity.

A volume is a factor, which we multiply. This can be more than 1, a larger volume, or less than one, a smaller volume, but always greater than 0.

In the case of a 4x4x4 inch cube, you need 16 as many lines, and 64 as many singularities (points), as you need to make the 1x1x1 inch cube.

You can extend this to other shapes, and wind up in a 5th grade geometry class.

Haven't you always been told you can create a ray from one point, or a line segment from two points, and so on. Have you ever really considered what length is the line segment you are creating, what length is the ray?