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Lite Applets - The Equiangular Spiral

Frank Wattenberg, Bart Stewart, and Suzanne Alejandre

This example is adapted from the module The Equiangular Spiral at the Connected Curriculum Project, which was published in Volume 1 of JOMA. In this variation the student uses an interactive Excel spreadsheet to fit an exponential function in polar coordinates to measurements made on a picture of a cross-section of a chambered nautilus shell. Then the student types the results into a form to see the curve superimposed on the shell.

As we did on the preceding page, we will start by opening a new browser window, this time with a simplifed version of The Equiangular Spiral. You can carry out the instructions in that page to see how a student might proceed. The Excel worksheet is opened from a link in the module page -- you can paste your own data into the worksheet, but sample data points are recorded there already. Of course, for student use, you would remove the sample data.  Start now .

Notice the power that this combination of a lite applet and Excel gives to students to investigate questions of their own. For example, students might wonder about the relationship between the volumes of successive chambers in the shell. They could investigate this by making various measurements on each chamber. If it appeared that the linear measurements seemed to follow a pattern, they might make an assumption about the missing third dimension and, based on that assumption, make a conjecture about the relationship between the volumes of successive chambers.

A new version of the complete Connected Curriculum Project module, The Equiangular Spiral, makes use of the Image_and_Cursor applet in much the same way as described here.

Frank Wattenberg, Bart Stewart, and Suzanne Alejandre, "Lite Applets - The Equiangular Spiral," Convergence (December 2004)