Day 40: Heart of Mathematics

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New assignment:

Fri

4/23

More Egyptian Arithmetic

Remember: If you do not attend the poster sessions (either your own or other peoples' sessions) you will lose 10% of the total grade for each day you do not attend and participate)

Order of presentations: here are your dates for next week:

Today: What can you do with only two fingers? (All things binary!)
- Today we look into more Egyptian arithmetic.
- Multiplication is accomplished through binary decomposition (successive doublings). Consider, for example, 57*63:
  
  1 63 *
  2 126
  4 252
  8 504 *
  16 1008 *
  32 2016 *
  64 too big!
  
  Now add up those rows marked with an asterix (*). You'll get the answer (3591).
- Division is also carried out in binary, but fractions make it more interesting: Why did Egyptians do things this way? (an example division problem, using binary)
- Let's start with a really easy one: 40 divided by 8.
- That was too easy: how about dividing 53 by 8?
- That was too easy (perhaps because 8 is a power of 2). Let's divide 53 by 7, in two ways:
  - Using multiple 1/7 terms, and
  - Using unit fractions
  - (and then showing how the first way can be re-written via the unit fraction table)), from the Rhind Papyrus (which dates to around 1650 BCE).
- Now you try: how would you divide 6 by 7?
- How about 47 divided by 9?
- What kinds of problems were the Egyptians encountering?
- How would you like to do story problems like this one?!
Links:
- Wikipedia on Egyptian Multiplication
- A division example, in some gory detail.

Website maintained by Andy Long. Comments appreciated.