Ah, tiles. You can get square ones, and do a grid, or you can get fancier shapes and do something altogether more complex. By and large though, whatever pattern you choose, it will normally end up repeating on some scale or other. That is, unless you go with something like a Penrose Wave Tile. Discovered by mathematician Roger Penrose, they never exactly repeat, no matter how you lay them out.

[carterhoefling14] decided to try and create Penrose tiles at home—with a 3D printer being the perfect route to do it. Creating the tiles was simple—the first step was to find a Penrose pattern image online, which could then be used as the basis to design the 3D part in Fusion 360. From there, the parts were also given an inner wave structure to add further visual interest. The tiles were then printed to create a real-world Penrose tile form.

You could certainly use these Penrose tiles as decor, though we’d make some recommendations if you’re going that path. For one, you’ll want to print them in a way that optimizes for surface quality, as post-processing is time consuming and laborious. If you’re printing in plastic, probably don’t bother using these as floor tiles, as they won’t hold up. Wall tiles, though? Go nuts, just not as a splashback or anything. Keep it decorative only.

You can learn plenty more about Penrose tiling if you please. We do love a bit of maths around these parts, too. If you’ve been making your own topological creation, don’t hesitate to drop us a line. 

If you’re like us, you’ve studied the mathematician [Euler], but all you really remember is that you pronounce his name like “oiler” and not much else. [Welch Labs], on the other hand, not only remembers what he learned about logarithms and imaginary numbers but also has a beautiful video with helpful 3D graphics to explain the concepts.

This post, however, isn’t about that video. If you are interested in math, definitely watch it. It’s great. But it also got us thinking. What would it be like to be a high school math student today? In our day, we were lucky to have some simple 2D graph to explain concepts. Then it hit us: it probably is exactly the same.

Changing the Subject

Well, maybe not exactly, but the problem is, we are guessing that your math teacher — no offense to him or her — wasn’t the same kind of person [Welch Labs] is. To be fair, we couldn’t have produced that video either. So, the way we see it, you have a few choices.

First, maybe you get lucky and you happen to get a teacher (about math or any other subject) who is just awesome. We are lucky enough to know a few of these people, but you have to admit world-class teachers are rare, and even rarer outside of colleges and universities.

Second, maybe you have a teacher who is greatly engaged and goes out and finds material like this to share. We suspect that goes on a lot, but maybe not as much as it could. There is a whole industry, too, set up to provide teachers with materials for profit, but it often isn’t at the same quality level as something like this. That’s unsurprising. If you are a movie studio, not every movie wins the Oscar.

Third, if a student is motivated, you have an extraordinary research library at your fingertips. Individuals create amazing articles, videos, and even courses. Major universities have their course material online for anyone to use, in many cases. You just have to find it.

A Mixed Bag

This, too, is a mixed bag. While you have access to more information, you have to critically evaluate if it is correct or not. You could presume anything you found in a traditional library was probably not patently false. Not that everything in a library is true, but, statistically, the way books used to be produced and library collections created, it was far less likely than finding false information on the Internet. On the other hand, how motivated were you as a kid to do things like that? Well, being a Hackaday reader, you probably were. Maybe a better question is how many of your classmates were in the library while you were reading about computers?

In a way, it is like tech support. Sure, AI might not be the best of all possible tech support. But it might be better than what you probably will get. Realistically, every teacher can’t be the greatest, and even if they were, they probably don’t have the time to produce huge amounts of high-quality material for their classes.

The Answer? (Or, at Least, the Question)

So what’s the answer? That’s where you come in. How could we make sure that all students get access to high quality resources from everywhere? I frequently hear of kids using Khan Academy, for example, to explain things they aren’t getting from their teachers. But that’s just one resource. Are there curated lists of resources for each subject out there somewhere? If not, why not? What other ways could we get the serious educational material produced on the Web every day into the classroom? I’m sure there are lists, but we’re thinking about something with the go-to recognition of, say Wikipedia. Not just a random blog posting. Let us know what you think and what’s already out there.

Maybe the best scenario is when great teachers share their materials with the world. We just need to get the word out. Another good scenario is when great teachers let their students take the lead. If you want to see how not to produce educational videos, have a look at this series of parodies of 1970-era science videos.