Augmented reality math is amazing and delightful

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This could be used to make a wonderful sand castle.


Since we’re watching this on a screen in 2D, I’m not sure I see the advantage over current technology. I can already draw a 2D projection of a spacial figure, and virtually rotate it, in the software on my PC.

From a pedagogical POV. I don’t think any new technology has a benefit over what you see in early-20th-century math texts, where figures are monochrome and hand-drawn. The old figures are technically less accurate, and lack much of the detail, but this is pedagogically a net positive, since the important features of the figure can be emphasized in the drawing through exaggeration and omission of distracting features.


For a static image, I agree. But I was immediately struck by the possibility of the surface being animated in real time as the underlying equation is altered. When combined with the ability to explore the resulting object in a natural way, it feels like we’ve crossed into something fundamentally more powerful.


We can already do that as well, though projected on a 2D screen.


You realize AR is stereoscopic, that is to say, true 3D, not 2D… ya?


Good point. The human visual system, especially in combination with kinesthetic sensation, would give an excellent ‘feel’ for what is going on. Certainly people who are naturally good at math (have good spacial imagination?) wouldn’t benefit as much, but for all the people who struggle to engage with math I think this would be a great benefit.


The only advantage of this kind of visualization, is that the parallax changes in synch with the screen. For 3D visualizations, that’s one more hack to add to the existing stereoscopic tricks and wooden models.

Like you, I don’t see this as a game changer necessarily, but the kids already have these smart phones in the classroom, so its beneficial for the teacher to give them something useful to do with those portable screens.

In before, “get offa my lawn!”


I realize that the video we were looking at is 2D, as I mentioned. I also realize that in a classroom situation, students are not going to be looking at it in 3D, at least for the foreseeable future. (In my classroom probably never, as even when I am teaching things like flows on surfaces this kind of representation is just not very useful.)

ETA: Of course, that you can do this very cool, I think the researchers behind it have accomplished something nifty, I just don’t see any real pedagogical value.

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Anyone who has looked at a pile of cryptic maths and a spaghetti diagram projecting some “salient features” into shrunken 2D plot may disagree.

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which is a slight deficiency in your imagination :-).

Imagine you run this on a smartphone, and you can look at the mathematical object from all sides by walking around it and using your phone as a window onto the object.

I’ve met a lot of highschool students who would benefit from this to get a grasp on the actual shape of the object and maybe develop some spatial awareness.


If 3D lacked such utility, I feel like we’d all have one big eye, heheh.

I’m a big fan of solid models for the kind of solids, especially regular solids, that most students encounter at early stages. I’m not sure many such students need to have a good understanding of the surface x^2+y^2+z^2=9-cos(2xy). But, maybe I just need more experience. I’ve only been at this, student and teacher, for 45 years or so.

Imagine you run this on a smartphone, and you can look at the mathematical object from all sides by walking around it and using your phone as a window onto the object.

If you mean using the smartphone in VR mode, mounted on the students’ heads in front of their eyes, then it would be interesting to see the hundreds of students in a Calculus lecture walking around the virtual object, and a neat trick if they could do it without too much damage to one another!

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augmented reality… CGI FX in near realtime?

This is the feverish dream of a TI graphing calculator of becoming cool at last.
Very nifty from a purely technical standpoint of course, and I would spend an inordinate amount of time just fiddling around with it.

That being said: it’s my theory that you can’t learn (or teach) spatial awareness. It’s something innate like, say the ability to sit through any opera lasting longer than 90 minutes or so. Help someone to become aware that they have it, and help them hone that skill - certainly.
And it’s no biggie if you have no spatial awareness whatsoever; you can always become an architect.

Without trying to belittle your experience or insights, to me as a practicing mathematically oriented engineer, the first thing I do when I’m trying to understand a new technique is to play with visualising the equations and some toy data. Often it makes much sense to do that in 3D*, then one struggles from the problem of actually seeing a 2D projection. This sort of tool would be super useful in some situations.

*Generally 3D is a better approximation to ND than 2D and me helps to build the mental model to understand the general case.

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Ok? You’ve been a teacher 45 years and you don’t see the usefulness of this? Maybe you’re just a better teacher than me and don’t need the visual aid, but in my experience it’s always nice to have different tools to appeal to different students.

Why do such students need math at all, I ask you. Maybe better to quit teaching altogether?

No. I mean holding the phone in front of you as a window into an ‘aternate reality’. Sortof like Pokemon go.

I guess not having a clear idea of how you could use this explains not understanding the usefulness.

Then we’re back to 2D, and we are already able to effectively do this; there is plenty of software for taking a 2D projection of a 3D plot and moving it around/modifying the parameters in real time, and all without you yourself having to walk around and bump into the other students.