Intersecting Powers and Roots
Here is an interesting little question. Its answer is simple, and not hard to see just by graphing examples; yet the algebra is easy to get wrong, as we’ll see several times. And subtle errors deserve study.
Boxes, Whiskers, and Outliers
Last week we looked at one way to display data, the stem-and-leaf plot. This time, we’ll look at a very different one, the box-and-whisker plot, which summarizes the data more broadly.
Stems, Leaves, and Data
It’s been a while since we’ve written about statistics, so I want to start a short series about that. Here, we’ll look into stem-and-leaf plots (also called stemplots).
Adjoints and Inconsistency: A Questionable Test
(A new question of the week) Last week we looked at how the adjugate matrix can be used to find an inverse. (This was formerly called the [classical] adjoint, a term that is avoided because it conflicts with another use of the word, but is still used in many sources.) I posted that as background …
Determinants, Adjugates, and Inverses
(A new question of the week) Looking for a new topic, I realized that a recent question involves determinants, and an older one provides the background for that. We’ll continue the series on determinants by seeing how they can be used in finding the inverse of a matrix, and how something called the adjugate matrix …
How Can 3×3 Determinants Give Both Area and Volume?
(A new question of the week) A recent question asked for the connection between two different ways to use determinants geometrically: to find the area of a triangle, and to find the volume of a pyramid (or the area of a parallelogram and the volume of a parallelepiped). Last time we looked at what a …
How Can 3×3 Determinants Give Both Area and Volume? Read More »
Geometric and Algebraic Meaning of Determinants
A recent question led me to look back in the Ask Dr. Math archives for questions about the definition and deeper meaning of determinants. Next week, we’ll see another old question for additional background, followed by the new question.
Diluting a Solution: Math vs. Reality
Here is a little question about making a formula to dilute a solution; we’ll see how to do the algebra, and also how what we teach in math classes isn’t quite real.
Function Transformations as Composition
(A new question of the week) We have discussed transformations of functions and their graphs at length, but a recent question suggested a slightly different way to think about them.
Why Are Functions Defined as They Are?
Last week we looked at what functions are; but many students wonder why it all matters. What makes them useful? What makes functions worth distinguishing from non-functions? Why do we make the distinction we do? We love “why” questions, because they make us think more deeply!