Example 2.  Find the equation of the parabola that goes through the origin and the point .  Compare the parabola solution with the catenary solution.
Solution 2.

Plot the parabola solution.

The length of the parabola can be approximated numerically by using Simpson's rule.

The length of the parabola is easily computed using Mathematica's built in subroutine.

The length of the parabola could be computed analytically.

Notice that there is a difference between the length of the catenary and the length of the parabola.

We could plot the difference.  This is just for fun!

What is the maximum difference in the height of the catenary and parabola?

If the unit of length was feet, what is the maximum difference in the height of the catenary and parabola in inches?

In your home if the error made in construction was  1.7 inches  off in  6 feet  of height, would you have a concern ?

(c) John H. Mathews 2004