Nowadays conic sections are not part of the standard high-school mathematics curriculum in Ontario (at least ellipses and hyperbolas are not; of course circles and parabolas are present), but they are interesting and important curves in mathematics, science, and engineering applications. There are two ways to define an ellipse: (1) as the curve of intersection … Read more
There is one art / no more, no less / to do all things / with artlessness. — Piet Hein The merely poetic destroys poetry. — Vladimir Holan (This post first appeared at my other (now deleted) blog, and was transferred to this blog on 25 January 2021.)
One day a graduate student submitted some writing to me, in which she was explaining rates of change at the high school level. She made an interesting statement: The slope of a secant line joining two points $(a, f(a))$ and $(b, f(b))$ on the graph of a differentiable function $f$ is the average of the … Read more
I believe that the main reason that we procrastinate is that we don’t feel competent. We fear that our results will not be up to some expectation, and the fear paralyzes us. Or rather, in this era with abundant opportunities for diversion, we distract ourselves in wasteful activities so that we don’t have to face … Read more
My parents grew up in a small village in the hills of Calabria, Italy. My Mom used to tell stories about her childhood, which involved getting up insanely early to hike out to work the fields with her father and older brother and sister. They would carry their lunch with them, which often involved only … Read more
I read this while browsing in a store in Ellicottville the other day: An actor included the following provision in his will: When he died he wished to be cremated, and then 10% of his ashes should be thrown in his agent’s face. Funny, eh? It says so much. The Sufis used humorous stories as … Read more
Once upon a time I was playing catch with a small child. The child was just learning to catch a ball, and so I drew closer to her because she dropped the last one I threw. However, the dear child was habitually teased by an older sibling for being a “baby” and she was therefore … Read more
I heard an interview this morning on The Current, and the guest (whose name I didn’t catch) spoke about VVIPs. Yikes! I had never heard this usage before, and I fear I am frightfully behind the times. I had better get up to speed before VVVIP becomes common. And how long can it be before … Read more
I was skiing today, and having a lot of difficulty getting down the hill. My son Jasper was doing his best to help me with advice as I kept picking myself up: “Dad, this is the way you learn; you just keep falling down over and over again until you get the hang of it.” … Read more
My wife and I saw the movie The King’s Speech (the official site is here; also see here) a couple of days ago, and it was very moving. I knew the outline of the story, and have always had great admiration for King George VI and Queen Elizabeth for courageously staying in London during the … Read more