540.30 Four-frequency Hyperbolic Paraboloid

540.31 A flat, four-sided frame (4) can be folded to define a nonplanar hyperbolic paraboloid (B, C, D).

540.32 The edges of the four-sided frame are joined with lines parallel to its edges. This forms the basic grid of the hyperbolic paraboloid. When the frame is in planar position (4), all the grid lines are of equal length. As opposite vertexes of the frame are lifted, the grid lines change lengths at unequal rates. Figure 540.30 is a four-frequency system that in closed position (E) reveals there are two different cross-lengths in addition to the length of the frame edge. Although the lengths shorten as the altitude increases, there are always only two different cross-lengths for a four-frequency hyperbolic paraboloid. The moment the four-sided frame is no longer planar, the fact of two different axis lengths is revealed.

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Fig. 540.30 Hyperbolic Paraboloid: There are always only two different cross-lengths for a four-frequency hyperbolic paraboloid. As opposite vertexes of the frame are lifted, the grid lines change length at unequal rates. The moment the four-sided frame is no longer planar, the fact of two different axis lengths is revealed.