Shade balls, sphere packings, aperiodic tilings, and crystallography!

I'm writing this in October 2020, and I'm teaching Intro to Materials Science and Engineering to the second year (3rd semester) undergrad students at IISc. I'm not thrilled with any of the options that I'm using for online teaching -- Microsoft Teams and all the stuff that comes with it (OneNote, etc.).

So, I am now back to Blogger.com to start posting stuff for my courses, and let us see how this experiment goes. Maybe it'll go better than Teams, simply because I have some familiarity with this platform.

Let me start things off with a couple of videos from Veritasium's Derek Muller for the module on crystal structures. While one of the videos is worth watching for the sheer fun, I also like the other one for the way it packs, within ~15 minutes, some four centuries worth of research in physical sciences and mathematics.

I heard about something called "shade balls" through this video:

And, here's a screenshot from the video showing 2D arrays of shade balls. When I saw it, it just blew my mind.

BTW, Muller has a follow up video on these shadow balls; this one is also a lot of fun. Here's a screen grab from this video showing a perfect hexagonal array of a mono layer of balls floating on water; the balls in the previous figure were in two or more layers.

The second video is pretty impressive. It's starts from Kepler's ideas about platonic solids and his sphere packing conjecture (which was proved and became Kepler's theorm only in the last 25 years or so), and takes us to the realm of aperiodic tilings with Penrose making an appearance in the last third of the video. It's pretty interesting that Roger Penrose's Nobel Prize announcement arrived about a week after Muller uploaded this video -- I should hasten to add that Penrose's Prize is for his work on black holes.

Anyways, here's that video: