I was pretty excited yesterday when the latest issue of NCTM’s Mathematics Teacher arrived in the mail and the cover story was an article I co-wrote with a former student who’s now at MIT.
The topic was the finding and proof of a cool interconnected property of the foci of hyperbolas and ellipses that I made years ago when setting up my TI-Nspire CAS to model conic sections via the polynomial definition.
After pitching the idea to teachers at professional conferences for a couple years with no response, I asked one of my 9th grade students if she’d be interested in a challenge. Her eventual proof paralleled mine, and our work together enhanced and polished each other’s understanding and proofs.
You can access the article on the NCTM site here.
While a few minor changes happened after it was created, here is a pre-publication proof of the article.