Bombadil Posted July 17, 2008 Report Share Posted July 17, 2008 They are fine but they don't answer my original question. I have no idea as to why you should want this “hyperplane” as part of our discussion. I suspect that it is a misunderstanding as to what a boundary is I was under the impression that the two ideas where related. I am not sure here but I definitely get the impression that you seem to miss the point of algebraic substitution. All that I am saying is that we should decide on which way to write the equation and not constantly change the way we write it. It just seems more convenient to stick with one way of writing it so as to avoid confusion as to why someone is writing it differently. Your concept of rotation is totally dominated by your intuitive understanding of three dimensional relationships. As I said to you long ago, the human mind has no experience with four dimensional relationships so we must be very careful. We cannot use our intuition at all and must depend upon analytical geometry, not mental pictures. How is the point at which the rotation angle is measured defined and is such a point always stationary or can such a point move during a rotation? Also are there any other properties that would seem that they would hold for a rotation that don’t hold in more then 3 dimensions? So in your proof one of the lines that define the plane of rotation is orthogonal to all previous planes of rotation (this line is in fact the axis just added) while the second line defining the plane is the line on which the projection is made onto. This results in a scaling of all of the points except one when a rotation is performed. Quote Link to comment Share on other sites More sharing options...
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