π from Collisions

  One of my sons sent me the link to the videos below. They show a very unusual way to find the digits of π. The problems and its two solutions show the connections and the interplay between mathematics and physics. The quality of the illustrations and the verbal explanations are excellent. Here are the…

Asymptotes and the Derivative

What does an asymptote of the derivative tell you about the function? How do asymptotes of a function appear in the graph of the derivative? One of my most read posts is Reading the Derivative’s Graph, first published seven years ago. The long title is “Here’s the graph of the derivative; tell me about the…

Seeing the Chain Rule

Being a believer in the Rule of Four, I have been trying for years to find a good visual (graphical) illustration of why or how the Chain Rule for derivatives works. This very simple example is the best I could come up with. Consider the function  . (See figure 1. A tangent segment at  is drawn.)…