Monday, November 14, 2016

Conic Sections Through Folding

Last week I reported on creating hyperbolas using a paper folding technique.  If you check the picture to the left, you can see the results of the activity. 

I started by passing out the written instructions so they could get started.  Once they began asking questions about the instructions, I showed them a video out of you tube showing how to do the exercise.  After that, they took off and had a blast. 

I collected one of the papers to share the results.  Guess what?  It is possible to do the same type of thing so you produce an ellipse, a circle, and a parabola using a line or circle and lots of folding.  The parabola uses a straight line rather than a circle to begin with but otherwise it uses the same type of folding technique to create the final product.

For the circle and ellipse, the shapes are created inside the original circle but you see the shape based on the folds.  The only technology needed is either a compass or a circular object students can trace and a marker.  I used an empty disposable coffee cup to provide the circle.

If you are interested you can check out the instructions for all four at this site.  If you want to include a video which provides clarification on how to fold, check out You Tube.  This video explains creating a ellipse from wax paper and lots of folding, while this one discusses using the same technique to create a parabola.

Although having already made one shape, its much easier to follow the written directions for other shapes.  A couple of my students chose to start again when they realized they were not folding the paper properly and they were extremely happy with the results.

I loved the activity because it only required I grab wax paper from home and it really worked.  I am going to try the other shapes in a day or two just to see how well they work.  If you want, go check out the directions and play with this at home.  I think you'll find it is lots of fun.