Dear Math Central Experts, One day, we were discussing 3dimensional items. Is a sheet of paper considered a 3dimensional shape? Or is it 2dimensional as described by 8.5 by 11 size? Also, could you give me an example of a 4dimensional item or scenario? Thank you for your time and effort,
Jaclyn Evans If you look at a sheet of paper with a good magnifying glass you can see that it is not 2dimensional. We do at times, however, think of the surface of a sheet of paper as an abstract, 2dimensional surface. We use it to draw "2dimensional" 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 4dimensions 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 2dimensional world. Cheers,Harley
