Is it a parabola or a catenary?
Our logo is a mathematization of the SFUSD logo, which itself uses a facsimile of the Golden Gate Bridge, one of San Francisco's iconic landmarks. In our logo, the bridge is combined with a coordinate plane and the image of a parabola.
But is the curve of the Golden Gate Bridge a parabola? Or is it a catenary?
But is the curve of the Golden Gate Bridge a parabola? Or is it a catenary?
What is a catenary?
A catenary is the curve that an idealized
hanging chain or cable assumes under its own weight when supported only at its
ends. The curve has a U-like shape, superficially similar in appearance to a
parabola, but it is not a parabola: it is a (scaled, rotated) graph of the
hyperbolic cosine. Mathematically, the catenary curve is the graph
of the hyperbolic cosine function.
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What is a parabola?
A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram, but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape.
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So what about the Golden Gate Bridge?
This Sketchpad image shows the fit of a parabola with the Golden Gate Bridge.
The cable on which a suspension bridge hangs would, on its own, be a catenary curve. However, the weight of the roadway changes the curve. When that weight is sufficient and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the cable follows a parabola.
If the weight of the cable and supporting wires are not negligible then the analysis is more complex
You can compare the parabola and catenary curves using Geogebra here.
A lengthy explanation of bridges and curves can be found here.
If the weight of the cable and supporting wires are not negligible then the analysis is more complex
You can compare the parabola and catenary curves using Geogebra here.
A lengthy explanation of bridges and curves can be found here.
