Day 08: Heart of Mathematics

Last Time

Next Time

Announcements:
- Your estimation assignment is due today.
- For today, you were to have read section 2.2 of our text (Numerical Patterns in Nature -- Fibonacci numbers).
- Your problems, due next Friday:
  - Show how to express 1729 in base 2.
  - Explain why we can't express 1729 using base 1.
  - Show how to add 147 and 173 (both numbers expressed in base 8)
  - Bring one thing from nature that illustrates Fibonacci numbers
  - Problems from section 2.2: pp. 60-61, #16, 18, 20, 22
Last time, we began our "Number Systems" unit with bases.
- New Math (Tom Lehrer) -- lyrics
- We'll begin with a "magic trick" that you can use to entertain friends young and old, using these cards.
- How does the trick work?
Today, we begin thinking about another way of writing natural numbers: using Fibonacci numbers.
- 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, -- what's next?
- II.6: bunnies and Leonardo Pisano Fibonacci
  How many bunny pairs at the end of a year?
- Fibonacci Numbers and Nature:
  - Oddly enough, Fibonacci numbers appear frequently in nature (e.g. in pine cones).
  - dandelions (Here's a scanned dandelion)
  - Spirals in daisies:
- Fibonacci number decomposition and Fibonacci Nim

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