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In our research, we have been looking at another possibility for the perfect vortex reaction chamber. If we look at the formulas for the hyperbola and the ellipse we find that they are exactly the same except for the sign in between the x and y portions. In the case of the hyperbola, the figure is open and the ends of the lines never touch each other. In the case of the ellipse we have a closed curve which when rotated about the axis will yield a ellipsoidal container. We reasoned that the best container for a vortex would be the mathematical compliment or inverse to the hyperbola. A type of ellipsoid. The question became one of discovering the exact mathematical inverse to the the hyperbola. However, as the water vortex curve is a square hyperbola, the first thought is that the inverse is a circle which is the cross section of a sphere. This shape turned out to be a very poor container for a vortex, as a matter of fact it was the worst container for generating a perfect vortex. We went back to the drawing board and finally derived the exact inverse form. This form is an ellipse that has points that are exactly tangent to the significant points on the hyperbola. As we can see in the next diagram, we have an ellipse shape which is superimposed on the square hyperbola. The outline of the ellipse is shaded so that it can be easily seen. This ellipse is indeed the exact compliment to the square hyperbola. The vertex of the hyperbola is the focus of the ellipse, and the focus of the hyperbola is the vertex of the ellipse. The vertexes of the diagonal hyperbolas are just touching the narrow sides of the ellipse. The length to width ratio of this ellipse is one to the square root of two. We can call this ellipse a root two ellipse. 25 JANUARY-FEBRUARY 1989 JBR, Page 5PDF Image | IMPLOSION by Viktor Schauberger
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