Re: Fw: Distance between 2 points
Ralf Nieuwenhuijsen wrote:
> Pretty neat, Hawke.
thanks. I 'preciate it.
>I didnt mess with the angle, cuz I was wondering
>how I would do that for multiple dimensions.
well, anything other than 2d or 3d rapidly becomes
metaphysical or undefined.
first, let's determine how many dimensions we actually
live within. let's divide the world into the smallest
practicle unit of space, and analyze that entity.
we can call it a particle. now a particle can easily
have a physical location that bears upon another
fixed particle location. that would give you your
delta {x,y,z} (Dxyz). good so far, right? well that
particle exists only during a specific time frame.
so there is another dimension of existence. time.
so now you have delta {time_born..time_died} (Dt)
well that's great you say, we have a time vector now.
here's the question that'll stump the big boys:
define the angle of vector Dt in relationship to
the angle of vector Dxyz.
now, there are a few more states of existence that
a particle may have. (oh,JOY!)
a particle can have spin (Ds),and that dimension
exists independently of Dxyz, but is dependent
upon Dt. so, define Ds as
delta{time_spin_began..time_spin_ceased,
speed&direction_of_rotation,
rotationalacceleration}
where direction is (-) for ccw and (+) for cw and speed
is rev/s and rotationalacceleration is +-rev/s^2.
now, tell me the angle of Ds in relation to Dxyz and Dt?
another plane of existence for a particle is temperature,
(Dk= delta kelvin) which is dependent upon Dt and Ds
(after all, the spin may be producing the Dk) but not
upon Dxyz.
there are several more:
1>a particle can be charged (+/-,amount)
2>a particle can be magnetized (amount)
3>a particle can be accelerating (+/-,amount)
4>a particle can be stable or decaying
and maybe not last, defnly not least:
5>a particle can be emitting (radioactive)
(typeofemission,amount)
so now we need definitions of vector angles for 1..5
as well, for a total of how many dimensions of
existence for a particle?
if you can determine the angular definitions for all
these states, we can include them in the program.
if you cannot, i suggest we leave it with 2d/3d.
>However you can easily calculate distance of two
>points defined in 5 dimensions.
>And in one, is no problem also. Its just pos (a -b)
*distance*, yes. *angle*, no.
so i left out the definition of FindDistanceAngle
for 1d, since it doesnt describe a right-triangle.
we could define it as {pos(a-b),0} if you like.
for 5d, yes, distance=no prob. *angle*=BIG prob.
>Could we get angles to work in any number of dimensions.
>In theory, giving 2 dimensions, you will get {distance,angle}
>Giving 3 dimensions should give you {distanze,xyangle,zangle}
>And with 4 dimensions we should get
> {distanze,xyangle,zangle,more_angles}
define more_angles, as per above???
> Oh yes, Hawke, I forgot all about that.
'tis ok :) you've corrected me, politely, many times
when i fergot sumfin... i call 'em 'brainfarts'. :)
speaking of forgetting:
<code snippet, previous post>
if length(temp)=2 then
for i=1 to len do
temp=dist[i]
adj=temp[1] opp=temp[2]
--below is what i had in mind
dist[i] =hyp2d(opp,adj)
--***look here:
theta[i]=arctan(opp/adj)
end for
ummmmm what should we do if adj is 0?
if it's zero, theta is *not* zero, in theory,
theta is *undefined*, is it not? :>
*thmoke! thmoke! i thee thmoke!*
--Hawke'
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