Day 12, MAT115

Last Time

Next Time

Announcements:
- Just a reminder that we have our first exam Thursday, over everything up to Fibonacci numbers. We review this week.
  You can use handwritten notes during the exam, as well as a calculator. Remember phone calculator etiquette: keep it out in front of you, in calculator mode.
Last time:
- We reviewed the quiz, and so did a few more examples of Mayan and Babylonian numbers.
- We played a game of the binary card trick (Fraudini's magic trick).
- In a game of Fraudini Nim, we saw Rachel send her professor down to inglorious defeat, forcing him to relinquish a precious sleeve of Thin Mint cookies (his favorites).
- We did several examples of binary factorizations, and then prime factorizations. We tested for "primality" -- is a number prime? -- by first taking square roots of the number, to see how many primes we needed to check.
- We talked a little about triangular numbers, and squares.
Today's Question of the Day:

Are we readier for the exam?
- Graphs: trees, complete graphs, simple graphs,
- one-to-one correspondences: primitive counting, tallies, body counting, cairns, knotted strings, etc.
- figurate numbers: e.g. 'rectangular numbers" (e.g. squares as sums of consecutive odd numbers), triangular numbers, tetrahedral numbers,
- Pascal's triangle (and variations, and all the number patterns contained therein.... and its uses....),
- prime factorizations; testing for primes
- binary factorizations and Fraudini's trick
- fibonacci factorizations and nim

Links:

Website maintained by Andy Long. Comments appreciated.

Fibonacci's solution in Liber Abaci,, chapter 12:
Because the above written pair in the first month bore, you will double it; there will be two pairs in one month. One of these, namely the first, bears in the second montth, and thus there are in the second month 3 pairs; of these in one month two are pregnant and in the third month 2 pairs of rabbits are born, and thus there are 5 pairs in the month; ...
there will be 144 pairs in this [the tenth] month; to these are added again the 89 pairs that are born in the eleventh month; there will be 233 pairs in this month.
To these are still added the 144 pairs that are born in the last month; there will be 377 pairs, and this many pairs are produced from the abovewritten pair in the mentioned place at the end of the one year.
You can indeed see in the margin how we operated, namely that we added the first number to the second, namely the 1 to the 2, and the second to the third, and the third to the fourth and the fourth to the fifth, and thus one after another until we added the tenth to the eleventh, namely the 144 to the 233, and we had the abovewritten sum of rabbits, namely 377, and thus you can in order find it for an unending number of months.