Dear Math Central Experts,

One day, we were discussing 3-dimensional items. Is a sheet of paper considered a 3-dimensional shape? Or is it 2-dimensional as described by 8.5 by 11 size? Also, could you give me an example of a 4-dimensional item or scenario?

Thank you for your time and effort,

Jaclyn Evans
Middle School question

Hi Jaclyn,

If you look at a sheet of paper with a good magnifying glass you can see that it is not 2-dimensional. We do at times, however, think of the surface of a sheet of paper as an abstract, 2-dimensional surface. We use it to draw "2-dimensional" objects like triangles and circles, but even these are mathematical abstractions. The line segments that form the sides of a triangle have only one dimension, length, but what we draw has a width, the width of the pencil line, and a height, the thickness of the layer of graphite that the pencil left on the paper.

A while ago we received a question about 4-dimensions and the reply by Walter has a description that you might find helpful. I would strongly recommend he book that he mentions called Flatland. It is dated, written in 1884, but the author attempts to give the reader a sense of dimension by describing life in a 2-dimensional world.

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