It creates an ominous sense of menace as the ellipses transform themselves into hyperbolas. I was in an ’80s mood, so I set this video to Jan Hammer’s song, Evan, from the Miami Vice soundtrack. By the way, Screencast-O-Matic has a new feature allowing the screencaster to add sound directly from your computer. Hot Text supports students as they learn to communicate their. Students develop deep conceptual understanding and confidence through direct manipulation of the geometry they construct, transform, measure, and animate. You can watch the results in the video below. Sketchpad’s environment is fundamentally geared toward geometric investigation and exploration. I had Sketchpad trace the blue line (as well as change its color based upon the length of segment DE). Point E moves around the circle, while point D moves bidirectionally along segment BC. The blue line is the perpendicular bisector of segment DE. Here’s the basic setup, if you want to do it for yourself: It was very tedious, but now Geometer’s Sketchpad can do it in seconds, as well as animate the “creases”. I used to use waxpaper folding to create repeated perpendicular bisectors that eventually resulted in conic sections. The locus of all points equidistant from a line and a point not on that line would be a parabola (but you already knew that if you had seen this earlier post!). For example, the locus of all points equidistant from a fixed point would be a circle. A locus is the set of all points satisfying some condition. Hmm, maybe there is something to these crazy conics after all….Īs my Precalculus students begin to explore conic sections, a related activity that is a lot of fun is to use the concept of locus to generate them. They got very excited as they saw their function plots match the photos so closely. Then, we pasted the photos into Geometer’s Sketchpad, placed a grid over them, and came up with functions that model each conic section. We took photos of the water coming out of a drinking fountain, the fireplace of our school’s library, and a flashlight’s beam when it is next to a wall. So, as my precalculus students wrapped up their investigations into parabolas, ellipses, and hyperbolas, we looked at some examples of how they occur in the real world. That said, I do try to make connections between abstract mathematical concepts and things my students encounter in their lives. I wonder if my colleagues who teach literature have to deal with that! Of course, math is worth studying in and of itself, just as poetry is. How many times have math teachers heard that question? I question the assumption underlying it – that math should only be learned if it has “real-life” application.
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