(*Junior high/ high school level*)

The mathematical formulas for the catenary and the parabola both
look easy. The formula for the parabola is a **quadratic
polynomial**, *y=k x^2*. Here, *k* is any positive
number, and "^" is a sign we use to denote exponents. So *x^2*
means "x raised to the 2nd power".

Experiment 3: On a computer or graphing calculator, or just by
hand, try plotting the function *y=k x^2* for different values of
*k* until you get a shape that looks like the shape of the Golden
Gate Bridge in the picture. What effect does changing *k* have on the
shape?

The formula for a catenary looks easy, but looks can be deceiving.

This is the **hyperbolic cosine** function, and we
pronounce it just like it's spelled, to rhyme with "gosh". You might
not have heard of it. But if you have heard of the exponential
function *e^x*, then we can write down *cosh* in terms of
the exponential function,

Experiment 4: On a computer or graphing calculator, try plotting
the function *y=k cosh(x/k)* for different values of *k*
until you get a shape that looks like the Gateway Arch from
the picture. If you use a positive value for *k* the curve
will be upside down to what the Gateway Arch is.
What effect does changing *k* have on the shape?

We said earlier that these curves -- the parabola and the catenary -- arise from considering all the forces acting on the hanging cables. We will talk more about forces in the next section.

Next: (Junior high level and higher): Forces - What Are They Good For?

Next: (High school level and higher): The Forces on the Cables.

Back: The Shape of the Bridge.

Return to the Golden Gate Bridge.

Last modified: Mon Sep 16 10:36:08 1996