Tag: mathematics

The problem of intersecting cylinders

Santino G.

The other day, I ran into a pleasantly difficult math problem concerning intersecting cylinders, the solution of which involved quite a bit of imagination. It took some time until the key insight dawned on me, but after that, the math was very straightforward. The problem is from the second edition of “Calculus With Analytic Geometry” by Howard Anton; accordingly, all credit goes to him for the exercise which I reproduce below (the solution, however, is my own): In the tradition of Sal Khan, if you haven’t already, take a stab at the above problem before reading my solution. Soln. To … Continue reading The problem of intersecting cylinders

Novel interpretation of the Delta-Epsilon Proof (maybe)

Santino G.

While writing my calculus blog, I found (perhaps even discovered) a new way of thinking about the – (delta-epsilon) proof. This interpretation won’t cause any kind of epistemic revolution in mathematics, but I believe it’s a helpful pedagogical tool worthy of its own blog post. In case you have forgotten, the limit definition states the following (where and are real numbers): To prove a limit statement, we have to show that the limit satisfies this definition. How do we do this? We assume exists and show that, no matter what the value of is, there exists a corresponding . The … Continue reading Novel interpretation of the Delta-Epsilon Proof (maybe)