[thechat] the political compass

Judah McAuley judah at wiredotter.com
Thu Jun 13 10:54:01 CDT 2002


martin.p.burns at uk.pwcglobal.com wrote:
> Results in order of simple distance from the centre (ie total of 2 numbers,
> not a vector. If someone can provide me with a simple Excel-like formula
> for calculating the polar co-ordinates I'll do real vectors):

No polar coordinates necessary.  Just find the distance from the center
point (0,0) to the desired point say (-3.4, -4.5).  Using our magical
Pythagorean theorem, the equation is Sqrt(a^+b^2) or in this example,
Sqrt((-3.4)^2 + (-4.5)^2) = Sqrt(11.56 + 20.25) = Sqrt(31.81) = 5.64

Note that this is the magnitude (or length) of the vector.  The real
vector is just the line from the origin (0,0) to the point in question
(-3.4, -4.5). The magnitude tells us how far someone is from the center
but it does not tell us left, right, up, down, etc. since it is a
combination of up and down and right and left.

What the magnitude does allow us to answer is the question: who is
farther from the center, someone who is at (-3.4, -4.5) or someone who
is at (-0.4, -7.5).  Both of those add up to the same (-7.9) but their
magnitudes are not equal.  As to the actual question, which is farther
from the center, that is left as an exercise for the student. *grin*

Judah




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