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The Tiniest Changes Add Up: How Infinitesimals Preserve Constant Area in Geometry and Unit Elasticity in Economics

~ Josh Fialkow ~ Leave a comment

In our previous post, we found that area cannot be maintained through equal but opposite percent changes in length and width using algebraic techniques. We determined that when we increased length by a certain percentage and decreased width by the same percentage, our new area calculation was derived through a downward sloping parabola of the … Continue reading The Tiniest Changes Add Up: How Infinitesimals Preserve Constant Area in Geometry and Unit Elasticity in Economics

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

~ Josh Fialkow ~ Leave a comment

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