Divergence, Curl and the Taylor Series Approximation

I wanted to examine two crucial principles in understanding the physics behind how systems flow- divergence and curl- and to fully explain both the mathematical assumptions and intuitions that underlie these bedrock foundations of field motion. I think what is most often overlooked in the explanations of divergence and curl is the fundamental importance in … Continue reading Divergence, Curl and the Taylor Series Approximation

Algebra’s “Constant” Problem: Why we can’t Maintain Constant Area Given Equal Percent Changes in Length and Width

As a teacher of SAT Math problems, I was stumped when I thought about the implications of the following SAT math problem more deeply: what happens to the area of a rectangle when its length increases by 30% and its width decreases by 30%? Solving the problem itself is algebraically straightforward. We start by letting … Continue reading Algebra’s “Constant” Problem: Why we can’t Maintain Constant Area Given Equal Percent Changes in Length and Width