From Transformations to Symmetry
Having looked at geometrical transformations, we can now apply them to the idea of symmetry. We’ll focus on symmetry of figures in a plane.
Slides, Turns, and Flips: How to Combine Them
Last time we looked at what it means to translate, rotate, and reflect figures on a plane. Here, we’ll look at some questions about what happens when these three transformations (and a fourth, the glide reflection) are combined.
Slides, Turns, and Flips: Transformations in Geometry
Some recent questions have dealt with translation, rotation, and reflection of geometric shapes, so it may be time to look into what we have said about that in the past. Here we’ll look at the meaning of these terms, at levels suitable for both kids and adults, and next time we’ll see what happens when …
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What If: Inventing “Pseudo-Complex” Numbers
We’ll work through a textbook exercise that encourages students to discover what it’s like to invent a new number system, as well as why some ideas work but others do not. The topic: What would happen if we changed the definition of the imaginary unit i so that its square is 1 rather than -1?
A System of Exponential Equations
What do you do when you are given a problem that starts with a “lie” and ends with a wrong answer? We’ll go in several directions with this problem, a system of two exponential equations in two variables.
Rolling Dice: Three Probability Problems
Last week we examined three probability problems that had problems. Looking further back, I find that Jonathan, who asked the first of those questions, asked a group of questions about rolling multiple dice in 2022. They provide some additional lessons about easy mistakes to make.
How to Think Through Probability Problems
It’s been a while since we’ve looked at probability. Here, we’ll look at three questions that we received last year. In each case, we have to detect an error! They’re good examples of what can go wrong, and what to do when your answer appears to be wrong.
When Percentages Don’t Make Sense
Last week’s question led to a number of previous questions, which would have made it too long. Here we’ll look at the last couple references we gave, dealing with percentages of a negative base. This time, the problems will be mostly about money.
Percentage Change in Temperature?
Continuing to look at past questions that didn’t make it into the blog, I find a question about percentage change in temperature, which nicely ties together a couple older topics that have long been on my list to cover. Let’s do that now.
Fun With a Functional Equation
Looking back at interesting questions I had to skip over when there were too many to choose, I found this interesting discussion of a functional equation.