2013-04-02, 11:25 AM
MountLag Wrote:I set them equal to each other is because we are assuming change in range is equal. So I did deltaR = deltaR -> A*deltaX = B*deltaY -> deltaX = B*deltaY/A -> deltaX = B/A when deltaY=1.
The result from your last pic goes deltaR = A*deltaX -> deltaX = deltaR/A. Substituting deltaR=B*deltaY in gives deltaX=B*deltaY/A -> deltaX=B/A when deltaY = 1, which would give the same result as what I did.
I just treated dX and deltaX as interchangeable because I was lazy. Thanks for showing that they really are interchangeable with that integral down there.
The changes (deltaX and deltaY) being proportional is definitely true; "setting the partials equal to each other" was just a mathematical miswording, I suppose, because it doesn't say what you meant to say.

