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INFINITY 3: Refining our Definition of Infinity

Math Circle 11.25.2014

(November 25, 2014)  Rather than my conventional in-depth play-by-play, this is a quick report on the highlights of our last session.  With the Thanksgiving holiday, 2 kids were absent, so our group  size was 5.

 

MATH RED LIGHT GREEN LIGHT, CONT’D

This week, we switched to “snails,” vs. live humans, as the playing pieces in our game.  Everyone adopted one and named it.  One of my helpers, L, led the game (thank you!).  By using smaller playing pieces, everyone was able to advance to near the finish line.  Therefore everyone was able to see what was going on there.  Therefore, everyone had the realization that once we approach the finish line, the halfway point between a player’s current position and the finish line would eventually become impossible to occupy without also occupying the finish line.  The students’ unilateral conclusion:  the playing pieces are still too big.  We need to try something smaller.

(If you haven’t seen the past 2 reports, click here and here for an explanation of how the game is played, and for our students’ take on the game.)

 

SINGING BOWLS

Asha Larsen (Talking Stick’s Maker Exploratorium leader) visited with her very large singing bowl.  She demonstrated it and let kids try it.  Then the kids came up with a list of why singing bowls could be relevant to math circles.
FUNCTION MACHINE

Then my other assistant J helped to co-lead a function machine activity, as L took some great photos. (See the photo gallery.)  The “rule” that the students had to discern was +2, which the kids verbalized as either “adding 2” or “you skip 2” once they figured it out.  Things got interesting when we used infinity as the input.  What is ∞+2?  Some said “googleplex” (or “googleplus”), some said infinity.  We debated whether something could be 2 more than infinity, and even voted on it (3 said yes, 2 said no).  Then we discussed whether infinity is a number.  No one in our group thought that infinity is a number.  (Impressive, since many much older students I have worked with over the years believed that it is.  I wonder why that is.)

 

CAT IN NUMBERLAND

All throughout class, the students were asking me, hoping, that we’d read more of this book, so we read chapter 2.  It was so engaging that we ended up going over our allotted hour for class.  (Sorry if I held your family up;  I’ll watch the time more closely next time.)  I can’t say enough about how good this book is.  It’s written in a very entertaining way, but more importantly, the author Ivar Ekeland explains the mathematical concepts in ways that these very young children are understanding.  Some credit goes to mathematician David Hilbert too.  Ekeland explains in the author’s note that Georg Cantor “may have been the first person ever to understand infinity,”1 but that Hilbert was the one to come up with a way to explain it.  Ekeland uses Hilbert’s hotel infinity metaphor to make this topic approachable for everyone.

Rodi

1 The Cat in Numberland, Ivar Ekeland, p60

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