Day 18, MAT115

• This session will be captured on Zoom, if I remember to turn it on, and record it.

  Our page of zooms and the play-by-plays.

• Roll

• We played a few "games" involving planar graphs and Euler paths (and circuits).
  1. When we have an Euler path (two odd vertices -- need to start at one, and end at the other).
  2. When we have an Euler circuit (zero odd vertices -- start and end at the same vertex).
  3. Euler's formula (for planar graphs): $V-E+F=2$

• What questions do you have?

We're going to do three things today: solve two mysteries, and celebrate our hero Zero.

• Have you ever seen this t-shirt?
  

  Now you should get the joke. And I'm hoping that, by the end of the day, you'll have come up with some more joke shirts!

• We begin by playing Sherlock Holmes in Babylon

  The author, Prof. Buck, guesses that "the document" (actually a clay tablet) comes from the city of Nippur, in what is now Iraq:

  

  Buck says this "Confronted with an artifact from an ancient culture, one asks several questions:

  1. What is this and what are its properties?
  2. What was its original purpose?
  3. What does this tell me about the culture that produced it?
  So: this is a representation of a clay tablet, with markings in it.

  Your job: to describe the markings, and investigate the patterns on this tablet.

  • What can we deduce about
    • the purpose of the table?
    • the way (and reason) Babylonians wrote their numbers the way they did?
    • the Babylonians and place value?
    • the Babylonian's missing number(s)?
    • the Babylonian influence in our world today?

  • How would the Babylonians write these numbers:
    1. 47
    2. 573
    3. 1,60, and 3600

  ---

• The frequently unsung hero of the Hindu-Arabic numbers is the digit 0 -- a symbol for nothing! (The Babylonians can't distinguish the numbers 1 from 60, without some additional context -- they had no hero).

  Well let it be unsung no more! I hope that you'll enjoy this rendition of

  Zero, My Hero

  (favorite lyrics: "et cetera, et cetera; ad infinitum; ad astra¹; forever and ever")

  ---

• Now to the mystery of the Mayans.... Same questions:
  • What can we deduce about
    • the Mayans and place value?
    • the purpose of the table?
    • the way Mayans looked at numbers and their world?
    • the Mayan influence in our world today?

  • How would the Mayans write these numbers:
    1. 47
    2. 573
    3. 3600
    4. 14001