Yesterday Malia and I were discussing some middle school math material (she’s a learning designer for a video game company) and she mentioned this thing called a “point reflection.” Apparently this is another name for what I learned as “symmetry about the origin,” which is to say it’s 180-degree rotation about some point. In other words, it is not a reflection. Reflections reverse orientation, right? Why would you want to confuse kids like that, how are they going to figure out what a reflection is when you go and tell them some rotation is actually a reflection?
Did any of the rest of you learn to use the word reflection for this concept? Am I wrong here? Anyone know how long this term has been around? Who came up with it?
A little googling confirms that in fact this is a Regents approved concept. And I guess I can see where they’re coming from, a point reflection is the same as applying an ordinary reflection about your point on each line through the point you’re “reflecting about.” Similarly for a “line reflection” in 3-space you could draw all planes through that line and then reflect through the line in each of those planes to get a “reflection” on 3-space. But it still seems incredibly counterproductive to me to use this terminology.
Wikipedia seems to suggest a split in this terminology with Point_reflection and Reflection_(linear_algebra) agreeing with the Regents and Reflection_(mathematics) agreeing with me. The linear algebra article strikes me as particularly nutty talking about things like “non-orthogonal reflections.”