Hyperbolas from Straight Lines In this problem we construct hyperbolic shapes using straight lines. Punch equally spaced holes into the edges of two large plastic lids. Connect corresponding holes with strings of equal lengths as shown in the figure on the next page. Holding the string taut, twist one lid against the other. An imaginary surface passing through the strings has hyperbolic cross sections. (An architectural example of this is the Kobe tower in Japan, shown in the photograph.) What happens to the vertices of the hyperbola cross sections as the lids are twisted more?
Vertices of the hyperbolic cross section.
The vertices of the hyperbolic cross section get closer to each other as the lids are twisted more.
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