- Announcements:
- Reminder: please shut down your electronics.
- No class on Monday: MLK day!
- You will have a quiz next Friday, and it might have a problem or
two from your homework assignments. Keep tabs on that assignment page. I've added an assignment for today, which is simply to learn the card trick I'll show you today.
- Question of the Day: How do we recover the number of sheep from
the primitive count?
- Let's review what we've done from last time....
- Where have you used the idea of a one-to-one correspondence in
your own life?
- We saw how some civilizations have used body parts as counting numbers.
- Do you realize that we can think of tallies as a way of
representing numbers? (see p. 36)
- Let's review this unusual method of "counting by partitions" that
Patricia Baggett and Andrzej Ehrenfeucht described at the 2011
National Math Meetings (here's
the original document, from 1820, from which they took the idea). This is the idea that I call "primitive counting".
- Let's try this again: last time we used a mathematical concept
called a "tree" to figure out what the sheep owner would write to the
king. Suppose that you have 52 sheep.
- Now we'll also go backwards....
- Okay: now let's suppose that the king receives a report that a person has
1,1,1,0,1,0,1
sheep. How many sheep does the person have? We will want to see how to figure
this out in a couple of different ways.
- Reconstructing the tree, and
- by writing the number of sheep as a special combination of sums and products.
- Now, with a partner, pass a "secret number", written out in as a string obtained from "primitive counting", and see if they can decipher yours. You decipher theirs.
- We'll end today by learning a "counting card trick" based on counting. Your job:
to figure out why it works!
Website maintained by Andy Long.
Comments appreciated.