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Re: [Phys-l] Another t trivial question



On 01/04/2011 12:10 PM, ludwik kowalski wrote:
Suppose I create a 2D coordinates system that has three axes, at 60
degrees with respect to each other. It has three triants (what is a
better name three regions in such space?). Suppose I use this system
to describe rooms. Suppose the axes are labeled (a) for absolute
pressure, (b) for absolute temperature, and (c) for floor area. Is
there anything heretical in doing this?

Yes (in almost all cases).

There is a theorem that says you cannot map 3 dimensions onto
2 dimensions in a way that is one-to-one and continuous.

So ... except for the unusual case where your data was somehow
confined to a 2-dimensional subspace of the nominally 3-dimensional
space (pressure, temperature, area) ... something bad is going to
happen if you try to plot 3 axes in the plane.

Try it and see what happens.