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WolframAlpha says that X^2 + XY is a Hyperbolic paraboloid. Is it correct? It looks more like a foldy piece of paper than the signature saddle to me.
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I have looked at the Wikipedia definition of a "hyperbolic paraboloid" and it gives an equation of:
My immediate intuitive thought is that the expression you gave cannot be rearranged into this.
However what about a rotated version of this ?
The equation that Wikipedia gives for this is:
If a = b then it is not exactly the same as your expression, but bares some resemblance with an extra x^2 term.
If a is not equal to b in magnitude then a y^2 term seems to be needed to make it a proper fit to the equation.
At the time of writing I am not sure whether the expression you gave is another rotation or not possible with any rotation.
My guess at the moment is that it is not possible with any rotation. I do not know how to rotate the equation by an angle
in the +z direction in general, but I would have thought the y^2 term would be non zero.
This is just a guess though so I wonder what other members think about this.
Last edited by SteveB (2013-05-16 18:46:17)
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It is possible to transform the original wikipedia equation to the equation
Wikipedia stated that:
Now let a=b=c=1
We need a transformation such that:
It can be shown that the following substitution can be used to achieve this:
Using this transformation:
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