Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
On Jan 4, 2011, at 2:20 PM, John Denker wrote:
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 the absolute pressure, (b) for the absolute temperature, and
(c) for the 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.
I deliberately selected a case in which three coordinates are always
positive. Each positive axis begins at the origin, not at infinity.
Plotting three positive axes in 2D space is actually easier than in
plotting three positive perpendicular axes in 3 D space.