120-sided dice!!

Our d120s arrived!!

Here’s the unboxing:

We were pretty lucky to have gotten our order in before all of the publicity caused the number of orders to explode. Before the boys ran off to show their friends the new dice, we did a few projects. I asked the boys to think of a question that they thought would be interesting to study with the dice. They didn’t have a lot of time to think about it, but I just wanted their gut reactions anyway.

My older son thought it would be fun to see how far they rolled. We have several different types of dice around the house, plus a few 3d printed shapes, so we saw how far the different shapes rolled:

The “winner” wasn’t actually one of the d120s, but rather a pentagonal hexecontahedron that we’d printed from Laura Taalman’s blog:

Day 194 of Laura Taalman’s Makerhome blog – the Pentagonal Hexecontahedron

The Dice Lab actually makes a d60 in the shape of a deltoidal hexecontahedron, so – no surprise, really – they are way ahead of us!

My younger son wanted to use them to make binary codes. I didn’t quite understand what he meant, but we eventually decided that the odd numbers would represent a 1 and the even numbers would represent a 0. We rolled the dice to create some 5-digit binary numbers. Strangely, we rolled lots of even numbers:

Finally, we did a project that my wife suggested – how many rolls to you think it will take until we see a number that we’ve already rolled? Fun! We had a great time exploring this question.

So, some fun little projects with the dice. Now the boys are off showing their friends and using them for some advantage playing Magic: The Gathering 🙂

Oh, and just in case you’ve not seen the video about these new dice, here it is:

A fun coincidence with our “1/3 in binary” project

Saw this tweet from Matt Henderson (via a Steven Strogatz retweet) today:

It first reminded me of one of Patrick Honner’s blog posts from a few years ago:

Honner’s post plus a lucky coincidence with a Numberphile video inspired a fun project with the boys:

Numberphile’s Pebbling the Chessboard game and Mr. Honner’s square

It wasn’t until later in the day that a different thought about this graphic hit me – we did a project about this shape LAST WEEK!!

Revisiting 1/3 in Binary

Since I was looking for a quick little something to do with the boys tonight, I head each one of them take a look at the tweet and tell me what they thought.

My younger son went first – he had lots of neat thoughts about the shape and we eventually found our way to the connection between this shape and writing 1/3 in binary:

My older son went next – he didn’t see the connection right away, but we eventually got there, too (oh, and ugh, just listening to this video I realize that I misunderstood my son when he was talking about a geometric series – whoops, he did say the right definition).

Thank you internet – what a fun coincidence!