Geometry teacher and author of
Discovering Geometry: An Inductive Approach
From my classroom on the third floor of George Washington High School in San Francisco, California, my students and I look out through 24 windows that face the Pacific Ocean. When the sun is out, I have to pull the shades down so that I can use the overhead projector. So for years I thought about designing a "Cathedral of Geometry," using a stained-glass effect for the six columns of four windows that face the afternoon setting sun. This past spring semester, my students and I finally did it!
First I created a scale model of the windows, on which I constructed the basic "lead" line design I wanted for each window. I had three geometry classes in the afternoon, one with six groups and the other two with nine groups each, and I assigned one of the windows to each group. The groups worked on their window designs, adding their personal touches within the parameters I'd set up so that the complete set of 24 windows would have a unified look, theme, and color scheme.
Each window in the top row had a Gothic arch with a circle inscribed within the arch. Within each of these circles were between two and six congruent circles, each internally tangent to the outer circle and tangent to the congruent, adjacent circles. Each window in the second row had two congruent gothic arches with internally tangent circles. The designs within the circles in these top two rows focused on the types of geometric art featured in Chapter 1: op art; line, daisy, and knot designs; mandalas; and Islamic art.
The windows in the lower two rows had two congruent squares with inscribed circles. The designs within the circles of these lower two rows focused on the content from DG Chapters 1-12: inductive reasoning; geometry vocabulary and tools; the properties of angles, triangles, polygons, and circles; tessellations; area; the Pythagorean theorem; volume; and similarity. So just like the great cathedrals of the Middle Ages, the windows told a story.
My students did not have the training, time, or resources to create their designs in actual leading and colored glass, nor did I want to use a plastic-based leading medium and liquid glass stains because they can be messy and rather expensive. For a quick and easy medium that produced a very colorful effect, we used large sheets of tracing paper and colored marking pens. The students constructed the first drafts of their designs with large chalkboard compasses on sheets of butcher paper; planned the details that personalized their artworks; and carefully transferred everything to the tracing paper. Finally, they used the markers to color the regions, and they finished their work by using wide black markers to trace the lead lines.
We placed their work on the windows with masking tape and stepped back to observe the result: it was beautiful! Not only had 24 groups of students enjoyed combining their efforts to create a work of art, but they had reviewed the year's content. Projects like this can convert "math atheists" into "geometry believers."
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