Welcome to the engineering/math nerd nitpicky pet peeve corner. I am your host, me.
I am glad that the above LNM video exists, and that the creator wants to wade into some of the history of design engineering and fabrication in the 1970s vs more recently.
I do wish, during the expository narrative on the limits of 70s curve building tech, that the vid would use the phrase "constant radius" instead of the more ambiguous phrase "continuous radius," which to some engineering and math ears (and perhaps to others' as well) will sound very different from what the vid is trying to convey.
At least there is a definition of terms at 16m0s in the vid. Good form. But it's unfortunate because the term "continuous" is already used in math to describe lines and curves that don't have abrupt and janky changes in value anywhere along their lengths, regardless of whether or not their radii are locked to a single value.
Specifically, the video uses the phrase "continuous" to describe the situation along each individual segment of classic Arrow track: a plot of that segment's (e.g.) vertical radius of curvature along the track's length will be a flat line with no changes in value at all between one end of the segment and the other end. This is best described in the context of the video as a "constant" radius, rather than "continuous," as "constant" conveys exactly the point being made while "continuous" really does not. An individual segment of classic Arrow looper track with its constant radius bends will indeed be continuous in radius, but it is also true that other manufacturers' (e.g. B&M's) individual track segment radii will also be continuous, so there is no distinction there.
The distinction between them for the video's purposes is, of course, (1) the universal use of constant radius curves in classic Arrow track, and (2) the many points where the individual sections of track are connected together, which in classic Arrow's case ironically are often not continuous, whereas B&M's largely or universally are.
A quick Google search will show that the term "continuous radius" is indeed sometimes used interchangeably in engineering, patent authorship, etc. to mean a constant radius. The intent of that choice of phrase seems to be to convey that the radius is "continuously the same value" along the entire length of the curve. Not the craziest usage of a word, certainly. But again, there is already a well established term for that in math and engineering: "constant." And "continuous" is already a well defined and widely used term for something other than "constant." So while the English language is nothing if not inconsistent, there is no great reason to perpetuate ambiguous language in the engineering/math/tech realm at least.
The audience for the video is more general than tech folks. All the more reason to use language that is both accessible and accurate.
And that's all for today's top story. I wish you all a good day.