Most of your research topics are very good.  Now is the perfect time to start working on the next step.  Remember that you may need to IDS some of your materials, and waiting until a few days before may be unsuccessful.  For those that need to resubmit - do so by this Friday, 2/12.  If you do not, you will have 1/10 of the grade indicated on your topic submission.  

§3.1.3-

In light of the fact that we discussed the quadratic example in nine chapters in some depth, and that there's so much material to talk about in this second half, so I'm going to talk about other things and not discuss the mostly similar details for the quartic equation of Yang Hui   (One specific answer to someone's question, 190,000 / 108,000 is rounded down because they are trying to find digits - rounding down determines the digit value, rounding up is too high.)  "Celestial unknown" is merely the method of solving polynomials.  It is the method we discussed on Friday from the Nine Chapters and it is the method used by Yang Hui for the quartic polynomial.  Why is this method of finding solutions to polynomial equations not used today?  That's always a good question.  One answer is that it is not well known in the west, another answer is that it only produces exact answers if the answers are terminating decimals, and a final answer is if we want approximations, "Newton's method" is usually faster.  

When Liu Hui found that the area of a circle is greater than 314 64/625
square cun and less than 314 169/625 square cun, remember the diameter is 20 cun, so the radius is 10 cun.  So pi is approximated between 3.141 and 3.142.

The distinctions that Suzuki makes about Liu Hui not using similar triangles don't seem terribly important to me.  I think either what they did was equivalent to similar triangles, or they knew how to use similar triangles, but chose to do it this way.  I do not know if Liu Hui included a diagram or verbal explanation (the second seems sure, but a diagram is possible).  He must have included at least one.

I don't see what's significant about the problem of Zhu Shijie presented in Suzuki.  We will look at other work instead.  

I also don't know why Wang Hs'iao-T'ung chose the numbers he did.  Furthermore, I will also not say anything about him - we have more significant things to do.  (The problem is quite easily solved in modern methods by merely trying.)  Same for Chang Ch'iu-Chien.  

I do think the Chinese playing cards were similar in that they were small slips of paper randomised for game play.  I'm sure they didn't have any of the icons or images like ours.  

Printing was developed in China much earlier than in Europe, perhaps before 220 CE, but definitely by the 13th century.  

Aside from Shih Huang Ti in 221 BCE, I do not know of evidence of attempting to eradicate history again.  

The modern view of the real numbers doesn't come about until the 19th century.  On the other hand, if you haven't taken real analysis, you probably don't have a modern view of the real numbers.  Although the Chinese (and Indians) seem to have no concern with irrationality, their understanding of real numbers is probably mostly in-line with a current high school understanding of the real numbers.  

Cycles occur naturally - It's probably difficult to find the beginning of them.  But, with the Chinese remainder theorem, there is definitely more of an emphasis on cycles and remainders than elsewhere to date.  

Commentators usually aren't providing more problems, but are providing interpretations and more applications of the material.  

Given Chinese advanced levels of technology &c, why didn't they expand more?  I think they were more focused on building defenses and strengthening inside than expanding outward.