What is a Ratio, Really?
A recent question reminded me I hadn’t yet written about the complexity surrounding the definition of ratio (and related terms, like rate and fraction). Here are four questions about the words.
Month: July 2024
Finding Length of a Roll: Facing Reality
Last time we looked at how to find the length of material on a roll, making some necessary simplifications. Here, I want to look at some variations on that: first, about carpet in particular, and then about wire on a spool.
Finding the Length of a Rolled-up Carpet
One of the more frequent questions we had on Ask Dr. Math was about how to find the length of material (carpet, paper, wire, etc.) on a roll, knowing only the inner and outer diameters and something else: the thickness of the material, or the number of turns, or the original size of the roll. …
Finding a Locus: Algebra and Geometry
Last time we looked at the meaning of the concept of locus. This time, we’ll explore seven examples, from two students. We’ll look at both algebraic (equation) and geometric (description) perspectives.