Thursday, May 31, 2012

We Got Mail!

A few years ago I created this video describing the Hirschhorn Tile:

This beautiful tiling is one of the subjects (and the cover model!) of one of my GeomeTricks Aperiodic Patterns books:

Well, guess who found this video and got in touch with me? The very person who discovered this tile: Michael Hirschhorn! Call me a geometry geek, but that would be like Justin Bieber emailing my 8-year old daughter :-)

We've already had lots of back-and-forths, but here's a snippet of what he wrote about the background of how he got to this tiling:
Back in the early 1970's, the Faculty of Science here [in Sydney, Australia] set up a program by which kids from (what we call) high school in their second-last year (so aged 16 or 17 or so) were invited to apply to spend a week near the end of their school year (November) involved in a variety of projects (in Physics, Chemistry, Math, Biological Science, .. ) in groups of about six, led by an academic. (About 120 students were involved each year.) In 1974, Professor George Szekeres led a group on the (very optimistic) task of finding all pentagons that tile the plane (a problem, incidentally, which is not known to be completely solved even today.) I was a young and junior member of staff (27), and looked in at what they were doing. They very quickly (within a day or two) restricted their goal to finding all equilateral, convex pentagons that tile the plane.
The group found a cosine rule that holds in an equilateral convex pentagon. At about the same time, I noticed that in every tiling we knew, the angles came together as follows A+B+C=360 degrees twice for every vertex where 2D+2E=360 degrees. (Each angle occurs twice in such an arrangement, and 2A+2B+2C+2D+2E=1080 degrees =3 times 360 degrees.) I suggested that there may be a tiling in which  2A+B+C=360 degrees, B+2D=360 degrees and C+2E=360 degrees. The Professor took home these relations and our cosine rule, and with considerable amount of work (by hand) found the solution,  A=60, B=160, C=80, D=100, E=140 degrees. He brought in his solution the next day, we cut out many such pentagons, and discovered it really did tile the way I proposed! Four such pentagons together form shapes like little penguins that march across the plane in rows, and the rows fill the plane. And that is essentially where our discoveries ended. The students then wrote up the week's work, and presented it to a large audience on the Friday night. After that, on my way home in the car, I had the thought, "What happens if we put six of the 60 degree angles together?" And by the time I reached home, I suspected that I could continue the tiling to cover the plane. So I got out my 20 or so pentagons, and, lo and behold, it worked! 
Mike also showed me a Hirschhorn tessellation that I hadn't covered in my book:

And he also described an irregular, equilateral pentagon tiling that tiles just like the 9-sided "Bent Wedge" covered in the same book:

Even if you aren't into geometry, you gotta admit that these are some pretty pictures!

Anyone can design anything in 3D!

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Check out Tinkercad

Looking to explore something new in 3D design over the summer?

So... during this period between the announcement of the SketchUp sale from Google to Trimble to the date when the sale closes, I've had some time to look into some other design apps I've been hearing about. And yesterday I spent a while poking around with Tinkercad, which is great fun.

IMO, there are two main great things about Tinkercad - it's easy to use (and FREE!), which is great for those who find SketchUp overwhelming (such as kids in elementary school), and whatever you design can be easily sent to a 3D printer, like MakerBot. How cool is it for a kid to design a little robot and then get to actually hold it in hand? (Of course, you don't have to print anything, it's also fun just to design stuff!)

Here are a few interesting models I found on their "things" page:   
Here's a 3D birthday card which was printed:

I hate to compare Tinkercad to SketchUp - they are both 3D modelers but with different focuses. But here's my comparison anyway:
  • SketchUp is certainly more robust, can be scaled to any size project (tiny mechanical parts to entire building complexes), and the design features enable much more detailed modeling.
  • Tinkercad provides fewer tools but they are quite easy to use: drag in some primitive shapes, make some easy changes, add decorations, holes, etc. The printing export is simple, and if you don't have access to a 3D printer, you can send your model to one of Tinkercad's partners to have your model printed and sent to you.
Tinkercad is web-based, so nothing to install. It operates on WebGL, so they recommend using Firefox or Chrome. (However, for me it didn't work on Firefox but worked fine in IE, not sure why!) You need an account (also free) to save whatever models you create.

To get started with Tinkercad, their very fun website has Lessons - short, guided, tutorial projects that walk you through the 8 or 10 steps to create something. 

I think 3D printing is the way of the future, with more and more of these machines popping up in schools, libraries, and labs. It's becoming way more fun to be a kid these days! If the 10-year old me had been able to model and design my own toys (a large number of years ago), I wonder what sorts of things would have piled up in my basement....

Anyone can design anything in 3D!

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Tuesday, May 8, 2012

What's Coming in Our May Projects?

This is both a fun and practical month for subscribers to our Projects of the Month. The practical includes a project that shows how to replace a lot of components at once (not to say that's not also fun), and the other two projects deal with zombies. But you can be a zombie-hater and still enjoy these projects - they show how to create faces for the faceless, and how to make your characters speak to one another.

There are plenty of people in the 3D Warehouse you can use to populate your models. Google has provided many generic, 2D "cardboard cutout" people that are great to use because they have low file size, and always face you - giving the illusion of 3D without using a huge 3D model. But many of these people have no faces:


This project shows how to add faces to the faceless. (You don't have to make zombies, unless you're trying to get the attention of 10-year old boys.)

Zombie Chat
Once you have your zombies (or whatever creatures you decide to make), this project shows how to use the Text tool and layers to create a chat between your two, well, whatever characters they are. Play the quick movie below: 

Replacing Components
In this project you start with a set of identical windows, and add a flower box to just one of the windows:

Then you replace all of the flower-less windows at once, with the one that has flowers:
These are fun projects to get students interested in something other than the approaching summer vacations! Subscribe here.

Anyone can design anything in 3D!

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Zombie Chat

The kids in my SketchUp class have gotten into downloading the various people available in the 3D Warehouse. It's best to look for the 2D people (and animals and trees, etc.) because they have miniscule file sizes compared to the much more complex 3D people. And if created correctly, these 2D "cardboard cutout" people will always face you, no matter where you orbit the model. This gives the impression of 3D, while keeping your models moving fast.

But a lot of the Google-supplied 2D people are faceless - meant to be used to generically populate SketchUp designs.

So I showed the kids how to not only add faces and accessories, but also how to create a short movie that includes a dialog.
Both of these topics are included in the Projects of the Month, going out next week.

Anyone can design anything in 3D!

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