<p>Investigation Backpack05 – Oregon Bridges by Bob Albrecht and Brian Hanna ([email protected])</p><p>High School Level: Algebra II and higher: This is an opportunity for students to investigate the difference between a parabola and a catenary. A brief explanation of the catenary curve can be found at Mathworld on-line; http://mathworld.wolfram.com/Catenary.html. </p><p>The initial investigation can begin with students collecting data (simple x and y coordinates for points along the curved truss) from the blueprints of the bridges and perform data regressions on them to determine the equations of the bridge arches. I was not able to find a simple regression method for catenaries on the TI-84, so I decided to use a set of lists to compare to the regression for a parabola. In lists1 and 2 I put the x and y data from my measurements. In list 3 I input the function values from a cosh function I had guessed. In list 4 I calculated the least-squares difference between my cosh function and the actual data. I then redid this method for a parabola instead of a catenary. It took a little longer, but the results were fairly decent after I came up with a good cosh curve.</p><p>A follow-up activity is to have the students use lab stands or desks and tape to carry the ends of a chain or string. Students can then measure data points from one end of the chain or from the vertex and come up with the equation of the resulting outline of the sagging chain or string. (The word catenary actually comes from the Latin word for chain!). Regression lines can then be created for a parabolic and catenary model and used to compare to each other.</p><p>Middle School level:</p><p>A good lesson plan for younger students to investigate truss design can be found at the following website: http://www.salvadori.org/aobc/handouts/lesson_truss.doc</p>