## Sunday, January 12, 2014

### Calculus: Solids of Revolution

In about a week, I'll be working with my students on solids of revolution. (At least, I hope to be. My calc II class is too small right now, and could be canceled.) Patrick Honner's Math Photo post of three beautiful bottles exemplifying solids of revolutions inspired me. I looked up beautiful bottles on Google Images, and there are so many. Some of them are solids of revolution and some aren't. I wonder if my students would benefit by identifying which are which.

Maybe that could be a first step, and then drawing a curve they think would make a good-looking volume when revolved. Hmm... (Anyone know a super-easy 3D modeler we good put our curves in, and get visuals from?)

Maybe this Friday I can get some students to come in and work with me on making models of volumes (not volumes of revolution, though), like these that Bowman Dickson made, or these (both types) that Rebecka Peterson made.

1. "Anyone know a super-easy 3D modeler we good put our curves in, and get visuals from?"
One of my high school projects from long long ago did something like this. You could draw a Bezier curve using control points and then click a button to revolve it around a vertical axis in the middle of the screen.

There are probably better things online but, I went ahead and dug it up and put it online here:
http://deepeco.ucsd.edu/~hye/bezier/BezierCurve.html

2. Hi, Sue.

"Anyone know a super-easy 3D modeler we could put our curves in, and get visuals from?"

I don't know how easy these tools are, but thought I'd mention them.

Google SketchUp (GSU) has a free version and is pretty easy. The conic cross-sections on my own blog were made using GSU. I haven't tried creating a solid of revolution with it, but it might be worth exploring. (Perhaps the paid version might be required for the capabilities you are seeking.)

I haven't tried the following two tools myself, but you might want to try them:

Online 3-D Function Grapher
http://www.livephysics.com/tools/mathematical-tools/online-3-d-function-grapher/

gnuplot
http://www.gnuplot.info/

Also, Octave could probably do what you want. It is a free MATLAB clone, but it might be more than what you want.

3. I still don't know whether the class is a go. I'm waiting to find out before I invest time in anything like this. We did a lot of Calc I review this past week.

4. My favorite modeler is quick and beautiful. The minus is that you can't go back to your curve to change it. http://www.zefrank.com/string_spinv2/menu.html

Hao, your app is blocked by Chrome's security even after I allowed Java for the whole site.

5. You can create solids of revolution or other known cross sections on Google Sketchup, and then use a 3d printer to create the solids. We did this in our Calculus classes this year and it was pretty sweet. The kids can be very creative and some used really complex cross-sections.

6. Thanks for the idea! I will find out whether our campus has a 3D printer, and see what it takes to do this.