- Here is my personal musical take on the Chinese remainder theorem (The current home of RESIDUE_INT is here.)
- The other most famous contribution of classical China is Gaussian elimination for solving systems of linear equations, 16 centuries before Gauss. Stillwell will get to that in Sec. 6.2, and I will in a much later week on the history of linear algebra.
- Katz has a section on Indian contributions to trigonometry. Indian mathematicians from Bhaskara I to the 14th century worked at calculating tables of sines, etc., presumably for applications to astronomy and navigation. To this end they developed various approximation and interpolation formulas that are understandable today but must have been nonobvious and ingenious at the time.

This week's reading, especially the Islamic part, is full of unfamiliar and complicated names. It's good we don't have a final exam, right? I feel I ought to be providing some guidance as to which are the most important figures from the Islamic culture. My list is

- Al-Kwarizmi
- Omar Khayyam
- Avicennna and Averroes, who weren't primarily mathematicians (mentioned in long footnotes in the Medieval chapter)

- Fibonacci. I made an attempt to find out why Leonardo of Pisa is called "Fibonacci". Both Katz and Allen say that the name was not applied to him until the 19th century; Katz obviously dislikes the name and brings it up as seldom as possible. But Carl Boyer's history-of-math book says that it just means "son of Bonaccio" -- Leonardo being himself one of those rich merchants' sons that he and his successors made a living teaching, according to Katz p. 214.
- Oresme (Katz tells us to pronounce it "o-REM").
Betraying my physics
background (and my years as a calculus teacher), I
find him to be the most interesting figure of
this period. Apparently he was the first to draw
**graphs**of functions representing quantities other than positions, and had some understanding of the relations between position, velocity, and acceleration.

- Broken links
- The link to the PDF file about Hippias and the trisectrix (Lecture 3) has been fixed.
- Allen's link to Stephen Wolfram's essay on the history of mathematical notation is broken, but I found it. It is not specifically medieval, so try to work it in later if you don't have time to read it now.

- Remember that you have a book review
due soon, and a major term paper that you should have started working on
by now.
*Note to self:*Remember that you have to tell them what to do for the short "position paper" due in April. - I'm delighted that you are making good use of the eCampus discussion
forum. Those of you who have not got into the habit of checking it
frequently should do so. (
*Note to self:*Do that yourself!) Between the help you give each other and Ngoc's hard work on the homework, I have needed to do very little handholding. I have carefully avoided commenting on the "how much should we help each other" issue, waiting to see how it would play out, and I think you have all arrived at a sensible and mature middle ground.