Day 9, MAT115

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Announcements:
- Quiz returned. Here's the key.
- Your quiz for this week will involve writing numbers in any given base, and, in particular, Mayan numbers. There may be something about Morse Code, and trees.
- I just saw the Highlands Middle School production of Schoolhouse Rock, however, so I have to share with you the video of "Zero, My Hero", which they sang.
Here's our "Question of the day":

What is the secret of the Great Fraudini's magic trick?
Before we get to that, however, let's first review what we discovered about writing in different bases using trees:
- First, choose your base (20 for Mayans, 60 for Babylonians, and one could choose virtually any base, greater than 1): then
- the method is this:
  1. divide the number by the largest power possible,
  2. remove the most multiples of the largest power possible, then
  3. "do it again" with the remainder.
- Example: suppose that there was some crazy society that used 16 as its base. Maybe these folks use only fingers and toes, but not the thumbs or big toes! How would we write each of these numbers using that base?
  Assume that this "crazy society" uses our ten digits 0-9, then uses A, B, C, D, E, and F as the symbols for the next six "digits" (10-15):
  1. A
  2. B
  3. C
  4. D
  5. E
  6. F
  In this case we use powers of 16: 1=16⁰, 16=16¹, 256=16², 4096=16³,....
  1. 5432
  2. 22319
  3. 57005 -- this one is a hexadecimal joke!
  What society would be so crazy as to use a system with base 16? Ours, of course!
  We use "hexadecimal" numbers in almost every web page on the net. Colors are given by "RGB" -- Red/Green/Blue -- and the relative quantities of each. Web pages use 256 (16²) gradations of each, represented by a two-digit base-16 number. You will see one in this page (buried in "the source"): the color "#FFF8DC" means FF red, F8 green, and DC blue. What numbers are those?
- Schoolhouse Rock strikes again: Little Twelve Toes
And now for something completely different (well, it SEEMS completely different!): a visit from the Great and Powerful Fraudini!
- How does the trick work?
- Can you make the trick work? You should be able to do it every time!
- Try this with a neighbor.
- Here's the handout for the cards, if you want to print off another copy.

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