Day 04: Heart of Mathematics

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Announcements:
- Your first homework assignment (fun and games) is due Friday.
- Assignment (hand this in Friday, 9/12) : Estimate the following:
  1. How much do you spend in groceries for a year?
  2. How much gasoline do you use in a year? (CNN website) What percentage of your budget is fuel?
  3. How many times will you breathe today?
  4. How tall is the Lucas Administration building?
  5. The southbound lanes of I-471 are backed up from the Big Mac bridge at the Ohio river, to Nunn drive. How many cars are stuck in traffic on that section?
Review: A glance back at the games:
- Meanie Genie
- Fountain
- Dodge Ball
- Dot of Fortune
Today we start our unit on Estimation, with Section 2.1: Number Contemplation
- Motivation: We have trouble estimating
- In this section we find an estimate of hairs on a human body (among other things).
  - How do our authors make their estimate?
  - Do our authors seek to estimate the number of hairs well?
  - What is the objective of the authors?
- What are some of the fundamental mathematical elements of the estimate?
  - Collection of (quality) Data
  - Approximation of the body by geometrical objects with known characteristics.
  - Units and unit conversion
    - We need useful referents
    - Is one of your fingers three inches long?
    - Is a knuckle an inch long?
    - How many centimeters in an inch?
    - How many kilometers in a mile? (factors of 10 and English unit conversion)
  - Computation (putting it all together)
  - Bounding (that is, capturing the true value between two values)
  - Sometimes it pays to be rough!
  - Can we do a better job of estimating?
- Two things are important: an estimate and a bound (some idea of how bad your answer can be): e.g.
  A CNN-Opinion Research Corp. poll of 1,041 adults conducted July 27-29 found that 62 percent favor a timetable for withdrawing U.S. troops from Iraq, but 37 percent oppose setting deadlines. The results had a margin of error of plus or minus 3 percentage points.
- What is "the pidgeonhole principle"?
  - Have you ever played a game, perhaps at a birthday party as a young child, that relies on the pidgeonhole principle?
  - How do we know that there are two people on earth who have exactly the same number of hairs on their bodies?
    - Why do the authors exaggerate?
    - World Clock for Population, Illness, etc.
- Problems to consider (exercises in estimation):
  1. Do you have a temporal twin (someone who was born on the same day as you, and will die on the same day)?
    - Is there anyone who obviously does?
    - Is there anyone who obviously doesn't?
  2. How many ordinary dice would it take to fill this classroom?

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