Small Moments of Infinity

[Edit: This post was originally titled Vignettes. About two seconds after I posted it, I came up with a title I liked better.]

#1

On Monday I read The Cat in Numberland by Ivar Ekeland with my daughter at the library (thanks to a reminder about it from Sue VanHattum at Math Mama Writes).  We read it last summer when she was a new six and the kid was really excited to see it again.  She's at a better math comprehension level for it now and we consume it whole in a quiet, sunny corner of the children's section.  This time around we notice the title page with the cat looking at itself looking at the title page looking at itself looking at the title page...recursion!

Anyhow, the hotel owner is griping about Zero and how there's no room for Zero at the Hotel Infinity.  And, to top things off, the owner doesn't think it's a good idea for Zero to room with Number One at the Hotel Infinity because how will he tell them apart from Number 10? 

Luckily the numbers are personified in the illustrations.  Unfortunately the hotel owner doesn't seem to notice this.  My kid does, though.  She says [referring to the illustration of 1 and 0 next to each other, compared to the number 10]: "There are two heads [one for 1 and one for 0].  Ten only has one head." (The head on 10 was on the numeral one.)  Not that this has any direct math 'value' per se, but it was still interesting to me that she noticed this.

#2
I forget exactly which part of the book we were in at the time, but at some point the cat, who is always thinking and "trying to figure things out", wonders why, if the hotel is full now, there are always more rooms available. (Or something like that.)  The kid notices the infinity sign in the illustration (figure 8 on its side) and she starts tracing it in the air saying to herself: "It goes on, and on, and on, and on..."

(Here's an interesting review of the Cat in Numberland by James Propp which includes a fascinating discussion of math pedagogy in relation to this story.)

#3Still at the library, the kid is chatting up the librarians about the resident frog 'Henri'.  She asks how old the frog and it turns out she came to the library as a tadpole, in March a couple years ago.  The kids says, unprompted:

"Well, human months are actually frog years.  There are twelve months in every year, and twelve plus twelve is twenty-four, plus two more months, so that makes Henri twenty-six years old!"  [Never mind it's July, not May...the shocking thing for me is that we were so busy playing UNO and Shut the Box all last year that I completely neglected calendars.  Turns out she's figured it out by osmosis.]

#4
This morning, a summer virus with a fever (after a winter of no illness) has the kid on the sofa listening to the Charlotte's Web audio book.  At some point even that isn't enough to distract her from her discomfort so I head to the couch to entertain her.  She asks me to draw pictures for her (and graciously tells me I can use any of her sketch books that I want!).  I'm really not inspired to do draw but I remember something I saw recently on the Math Munch blog -- Vi Hart doodling musically/visual frieze patterns.  I've always been a doodler, so I decide to experiment with my own frieze patterns.  I'm not sure if they're exactly what they're supposed to be but they're fun to make.  I erase a few, especially the ones that look like they have eyes.  Too much for a kid with a fever!  The kid is absolutely thrilled with the ones we kept, especially the last two. 

I think the frieze patterns/designs have something to do with infinity, and so I end this post now where I began it, discussing recursion and infinity.  I love it when that happens!