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When Does 2D Become 3D?

Date: 01/20/2003 at 05:10:13
From: Caro
Subject: 2D versus 3D

Is a piece of paper a 3D object when held up in space? Or is it a 2D 
object in 3D space? Similarly, something like a CD-Rom? Is that 3D or 

When does 2D become 3D?

Date: 01/20/2003 at 12:24:14
From: Doctor Jacques
Subject: Re: 2D versus 3D

Hi Caro,

Strictly speaking, an atom occupies a non-zero volume in space (about 
10^-30 m^3), and therefore any physical object is a 3D object.

However, math is not about the real world.

In math, we define concepts and axioms, and we explore the logical 
consequences of these concepts and axioms.

When we use math to solve a real world problem, we start by building 
a mathematical model of the problem.

We try to include in the model all the relevant features (otherwise 
it will be useless), but we do not want to include all features, 
because the resulting model would be too complicated to handle. In 
other words, our model is a simplified version of the real thing, and 
the amount of simplification depends on the question we must address.

To take the example of a CD-Rom:

If we want to know how many bits can be written on the surface, we 
can consider it as a 2D object.

If we want to know how many CD's we can pack in a given box, we will 
consider it as a 3D object.

It all depends on the intended use of the model.

- Doctor Jacques, The Math Forum 
Associated Topics:
High School Euclidean/Plane Geometry
High School Higher-Dimensional Geometry
Middle School Higher-Dimensional Geometry
Middle School Two-Dimensional Geometry

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