Continuous Everywhere but Differentiable Nowhere

The beautiful New York weather and three day weekend inspired to go out on this Saturday night. So I shaved, dollied myself up, donned my newly purchased tote bag, and left the apartment.
I felt pretty good about everything as I was having dinner with a friend, followed by a postprandial drink at a local coffeeshop. [...]

The NYT has recently run two articles (one, two) on the fear that exists (among some) that the Large Hadron Collider — when started — will destroy the earth through the creation of a black hole. Interestingly, this was exactly the topic my undergraduate thesis (in STS) was on, except instead of being about the [...]

On the same blog, God Plays Dice, I learned two important things today:
(1) The Napkin Ring Problem, which basically says if you take a sphere, and cut out a cylinder from the center (and take off the two caps at the top and the bottom of the sphere), the volume of the remaining solid will [...]

This has been a stressful few days. In my school, we have to write comments on each student (about 1/2 page single spaced) and those are due on Thursday. In addition, with the end of the third quarter, there has been a massive grading effort on my part to finish up the video projects I [...]

I love it when my students think for themselves. 
When learning the law of sines and law of cosines — and when it’s appropriate to use one or the other — our textbook gives pretty prescriptive directions. For example, when you are given SSA (a side, a side, and an angle opposite one of those given [...]

In my trigonometry classes, I decided to deviate from the textbook ordering of concepts. The other teacher, thankfully, was on board. (And next year, I want to tweak things even more.)
Our textbook presentation of trig starts out with reviewing right triangles, SOH CAH TOA, and in the same section, introduces the reciprocal trig functions (csc, [...]

 
Monday Math Madness is over again. I got the right answer to the problem, but I didn’t win the prize (sigh). The solutions were all about the same, so I’m posting what I emailed below the fold…
 

In the past few weeks in my seventh grade pre-algebra class, we’ve been working on some hard problems involving inscribing circles in squares and squares in circles and, sometimes for good measure, playing around with equilateral triangles too. Radicals abound. And for the most part, I see them getting it.
But recently (for a number of [...]

In my last hastily written post, I wrote about the process of interviewing from the side of the interviewers. That’s because I’ve been heavily immersed in it for the past few weeks. But it wasn’t so long ago that I was on the job market myself, writing personal statements, meeting myriad people, and giving my [...]

This year I’ve been intimately involved with the hiring process. With two of our veteran (and funny, and quirkily snarky, and supremely excellent) teachers retiring and our department head moving on to bigger and better things, there have been a number of math openings to fill. I’ve now seen a lot of demo lessons, had [...]