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[My Name is Immaterial]

What's c*?

The constant c multiplied (* is used to denote multiplication) by the sine of angle theta.

[TheBiggerFish]

*

c is a variable, in this case, although it varies based on the triangle.

Do you know the Pythagorean Theorem?
a²+b²=c²?  (for right triangles)
That c.  Or that a or b.

[Graknorke]

Also can you even do that? Your triangle only has two dimensions, not three.

I was doing it in two dimensions just to show why the obvious answer doesn't work. Since in three dimensions I'd only be doing that three times anyway.

[wierd]

Uhm.... Wouldnt the displacement between two points just be the distance between the two points?

Since there are only 2 points, you just need to define your coordinate system to be a plane that intersects both points. (there are an infinite number of solutions, because 2 points produce a line, not a plane.)

This should be possible with simple geometry, I think.

This gets harder when you have a fixed axis system that you need to get values against though.

Hmm... 

How about a convolution on point slope notation derivation from the coordinates of the endpoints of the path you want the displacement on? 

Say we have 2 points a X3,Y2,Z0 and X-4, Y12, Z1

The first point has a point-slope notation that is easy, since it lives entirely in the X-Y cardinal plane. (X3,Y2--- Or, for every X, you get 2/3 Y, when measured through the origin.) For the second, it is a little more complicated-- For every -X, you go 3Y, and 1/4Z, when measured through the origin.  This should enable you to derive distances in X, Y, and Z to these points. Then you can use the pythagorian theorem to derive the missing distance between the points, after determining the angle of these two lines through the origin.

Right?

(You then have 3 points, and 2 lines, allowing you to define a plane-- allowing you to create a triangle.)

[MagmaMcFry]

Is there a way I could find the x y and z components of the square of the displacement between two points without using trigonometry? I think it's impossible but I don't know for sure.

Okay first of all displacement between two points is a vector, and the "square" of a vector is a scalar, so it doesn't even make sense to ask for the components of the square of a vector. Can you reformulate your question so it makes more sense?

[Shadowlord]

I was thinking csin was some variant I'd forgotten about. I'm feeling a little out of it today. 

I'm not sure why you are checking whether c^2 * sin(theta) = b^2. It's not supposed to. I mean, you have the square of each component, not the component itself, so of course that isn't equal. (I might or might not be talking sense here, I'm not sure.)

Is there a way I could find the x y and z components of the square of the displacement between two points without using trigonometry? I think it's impossible but I don't know for sure.

A displacement is the shortest distance from the initial to the final position of a point P.[1] Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A displacement vector represents the length and direction of this imaginary straight path.

You likely know all this:
a^2+b^2=c^2 is basically c=sqrt(b^2+a^2) or d=sqrt(x^2+y^2)
it's the distance formula in two dimensions, which you would expect since if you make the hypotenuse go from point 1 to point 2, c is the distance and a and b are x and y (or vice versa, the order is unimportant).
If you add a z dimension you have the 3 dimension distance formula, as I'm sure you know. d=sqrt(x^2+y^2+z^2).
Of course, you can't make a physical right polygon which has both an x, y, z, and h (distance) line, but you shouldn't need one.

Anyways, if displacement is a vector, you don't have any squares or square roots or the distance formula involved:
displacement = abs(p1-p2)
displacement.x is abs(p1.x - p2.x)
but you still asked for the square, so...

[Graknorke]

Is there a way I could find the x y and z components of the square of the displacement between two points without using trigonometry? I think it's impossible but I don't know for sure.

Okay first of all displacement between two points is a vector, and the "square" of a vector is a scalar, so it doesn't even make sense to ask for the components of the square of a vector. Can you reformulate your question so it makes more sense?

You scale the vector so that it's magnitude is squared, but direction remains the same.

[Putnam]

square its magnitude then

[MagmaMcFry]

Is there a way I could find the x y and z components of the square of the displacement between two points without using trigonometry? I think it's impossible but I don't know for sure.

Okay first of all displacement between two points is a vector, and the "square" of a vector is a scalar, so it doesn't even make sense to ask for the components of the square of a vector. Can you reformulate your question so it makes more sense?

You scale the vector so that it's magnitude is squared, but direction remains the same.

Then just multiply the vector by its magnitude (i.e. multiply each component by the magnitude, (x, y, z) becomes (x*sqrt(x²+y²+z²), y*sqrt(x²+y²+z²), z*sqrt(x²+y²+z²))). I'm still wondering what such a vector could be used for.

[sprinkled chariot]

While being in some rural places, I have found out, that mosquitoes there act in retarded way, they just fly straight to you, trying to get your sweet blood .
 Meanwhile mosquitoes in Moscow, dont fly all the way straight to you, but land on some object and walk the  final part of distance without flapping wings and emitting damn noise. Not only they do this, but they also use hit and run tactics with unreachable dark place under sofa serving as safehouse. Also they kinda prefer attacking legs, so you are not warned of attack before abomination sucks the life out of you .
How did those monsters get more advanced pattern of actions then rural mosquitoes? How does it get in new generation of flying assholes?

[Rolan7]

In discussion of the fundamental elements, what are the main differences between Air and Water?  In the greco-roman 4-element system.

I wonder because, in the 5-element asian system, air isn't present...  And water opposes Earth and Fire.
Okay "opposes" is a gross simplification, but for reference http://www.utahsymphony.org/blog/wp-content/five-elements.jpg

[Shadowlord]

It isn't based on anything sensible so I wouldn't really try to make sense of it.

[scrdest]

In discussion of the fundamental elements, what are the main differences between Air and Water?  In the greco-roman 4-element system.

I wonder because, in the 5-element asian system, air isn't present...  And water opposes Earth and Fire.
Okay "opposes" is a gross simplification, but for reference http://www.utahsymphony.org/blog/wp-content/five-elements.jpg

It's a 2x2 matrix of cold/hot and wet/dry, with the two you're asking for are both Wet and, respectively, Hot (because steam) and Cold. So, each element has a single opposed element and shares a trait with two adjacent ones. It's really not super deep, it was primarily a crude descriptive device to reason about properties of matter (which could contain those properties in various proportions).

[Graknorke]

What's the difference between a graphing calculator and a programmable calculator?

[Baffler]

What's the difference between a graphing calculator and a programmable calculator?

A programmable calculator has a basic sort of language that let's you automate things. A graphing calculator can graph an equation. They aren't mutually exclusive. in fact most are both.