A delayed response to feedback (while awaiting confirmation):  Someone requested that the exam be given in a computer lab so that you will not need to worry about power supplies.  I checked into this and there was only one computer lab with 40 computers (exactly 40, mind you).  Fortuantely, it was available for us.  Our exam will occur two weeks from now, Friday, March 12, 2010 10:00 AM - 10:50 AM in Milne 104.  I will try to remind you regularly.  Please do not appear here on that day.

§5.2.3- Quick Answers

The digits are probably presented in the order in which they come to mind: 0 9 8 7 6 5 4 3 2 1 (read right to left).  Alexander of Villedieu is not saying that one counts to 0 after 9, but in some sense he leaves the most sophisticated for last.  The point of the poem is to introduce Hindu-Arabic numeration.  It's my impression that between Leonard of Pisa and those we're seeing in France, Europe is basically getting to the point of having basically modern whole-number place value.  Decimals are still lacking, but I believe all else is pretty much in place, or settling in now.  As far as I can tell, the Ode to Algorithm does still exist.  Recall our reason for writing numbers with the low place on the right is inherited from Arabic.  

I want to talk about Rithmomachy.  Unfortunately, this is all I know, and I don't have time enough now to research it.   It's a two player game and the "rithm" part is connected to arithemtic.  It's a battle of numbers.  There are claims it goes back to pythagoras or at least Boethius, but the oldest evidence is from around 1030.  It was widely popular (moreso than chess for a while) until the 17th century.  Here is some more information.  I would really like to learn to play and to bring it to PRISM someday.  Anyway, here's some images (to add to Jordanus).  While it is said to be played by intellectuals and improves mental arithmetic, it was not merely a teaching tool, and was definitely played for amusement.  

Not all architects were mathematicians, but either they knew one or they were themselves, likely.  I don't know much about architecture, so I can't say much that isn't in the book.  Some of the buildings from then are still around - that says something about how well they were built.  


Jordanus Nemorarius is one person, but sometimes Suzuki probably gets bored writing the same name.   I don't know of anyone else using varaibles the way Jordanus does.  It is a step, but also has some issues, surely.  This is definitely one of the earliest uses.  Whereas there are other proofs that amount to existence proofs before this, Jordanus is more explicit in his language.  

Yes, the University of Toulouse remains.  

The quadratic formula, effectively in its modern form, has been known for over a thousand years before this time.  
  

The troubadours told tales loosely based on fact, like is still done today.  

Cathars were a Christian sect.

The King felt that Oxford University deserved compensation for the lynching of its students, so required the town to contribute to scholarships.  

Ptolemy and Archimedes surely did physics before this, and I am certain there are others, but those are the first to come to mind.  This is *not* the beginning of physics.  

Before printing, books were written (and copied) by hand.  

I do believe the permutation for sestinas was always (612453) (again, not what Suzuki says, and I think the 1-2 part is pretty important).

I think what we see here is more refining what is known (close study of old works) rather than advancing mathematics, hence Suzuki says it has stagnated.  

Review our day 1 notes for double false position, or read about it in Leonardo of Pisa.  

"One of my other professors saw me reading this text book and made a comment about how math is the only completely man-made science and I thought that was very intriguing."  Yes, and it's the only one that inspires as much universal agreement.  Because we humans made it, we humans tend to agree upon it more than anything else.