Revisiting Graham’s number

We had only a short time this morning for a project. At this point I should know better than to rush things, but I don’t!

Based on some twitter conversations this week I thought it would be fun to revisit talking about Graham’s number. We’ve done several projects on Graham’s number in the past, but not in at least a few years.

To get started, I asked the boys what they remembered:

Next we talked about one of the simple properties of Graham’s number (and power towers) -> they get big really quickly!

Here we talked about why 3^3^3^3^3 is already as about as large as one of the usual “large” properties listed for Graham’s number. Namely, you couldn’t write down all the digits of this number if you put 1 digit in each Planck volume of the universe:

Next we talked through how to find the last couple of digits of Graham’s number. This part of the project is something that I thought would go quickly, but didn’t at all. Still, it is pretty amazing that you can find the last few digits even though there’s next to nothing you can say about Graham’s number.

If you search for “Graham’s Number” in my blog or in google, you’ll find some other ideas that are fun to explore with kids. I highly recommend Evelyn Lamb’s article, too:

Evelyn Lamb’s amazing article about Graham’s number