Goals and expectations - what to take from the reading?

Take notes on the reading.   Our conversations will supplement them, but cannot possibly replace the breadth of the reading.  For each section you read, have some idea what mathematics they were doing and why.  Once we get to Greece probably take 1-2 people as particular examples that you find interesting and keep those.  You are definitely not responsible for all the details in Suzuki or everything that we discuss in class.  But, take enough of it so that you have a good collection of examples and motivations for reference.   

As regards to how accurate to know dates - in this very early material, to the nearest 500 years is pretty good.  When we get to chapter 4 probably to the nearest century and near the end we might care to the nearest decade.  We'll never care more than that.  

By the way - in case it's ever an issue - please do *not* submit reading reactions for a particular class until the previous class is complete (otherwise, I'll get quite confused).  

Quick answers 1.1/1.2

A recurring comment that I see in reactions amounts to "I don't like it - it's different from what I know".  Try to assess beyond mere familiarity - to something more significant.  What are the values of the other methods?  Consider the starting point - for our work today, that starting point is basically nothing.  As the semester goes on, think about what the work represents in contrast to the starting point.  

Also we have a long story ahead of us - don't expect direct simple answers to how we got where we are today.  If something reminds you of something we do today, it may have influenced it, but it's unlikely it's the sole and simple cause.  With regard to human history, the simple explanation is usually not the full truth.  

On the other hand, please keep in mind limitations of time and space.  Neither Suzuki nor this course has the potential of deeply understanding 4000 (not to mention 37,000) years of history.  There are lots of places where you'll want to know more.  One point is that those are ripe for topics for the final project.  And the other is that outside reading is strongly encouraged.  

Seems very unlikely to me that it is a coincidence that 11, 13, 17, 19 are all prime.  OTOH, they could just be odd for some reason and 15 was unlucky.  These lines are countable, and therefore they are math.  We think they are interesting math. because they are primes.  No ideas what used for.  

When Suzuki says that "an unknown group of people invented agriculture" it is possible that this "group" is not localised in time or space.  Could be several groups.

I'm guessing it's only a coincidence that Suzuki's made up symbol for river is also sometimes used in mathemaitcs - however it may also be because it was easily typeset.

Although Egyptians worked in something like base 10, they're work doesn't seem to directly lead to ours.  There's a long story leading to our current numeration.   Stay tuned.  

Our history of geometry will be broad in time and space.  Most importantly you will learn that it didn't begin or end with Euclid.  

I think there's no reason to believe that the Egyptians thought of inverses in anything like the way we do.  They surely did, though, understand that multiplication and division were opposites.

One answer for why Egyptians didn't work with non-unit fractions is that they didn't have notation for it.  Frequently notation limits things that way - you can't study something if you can't write it.  They never put the same unit fraction next to itself.  2/3 was probably the one exception because it is so common.    Another point is that 7/19 is, in some sense, merely a division question, not an answer.  

12 months - lunations, 365 days - averages of Nile flooding cycles (caused by solar cycles).  There's lots more history to get our current calendar - not directly from Egypt.  

There is not much actually known about how the pyramids were constructed.  This is why it is omitted.  

Ahmose was both the name of the scribe of the Rhind Papyrus and the first pharoah of the 18th dynasty.

Dates from one calendar can be translated into another by finding a common event.  Good choices are astronomical events (eclipses &c) which we can date very accurately.  

Suzuki isn't assuming that Egyptians had a symbol for one million - it is well known - the astonished man.  

There is no evidence of trigonometry as we know it in Egyptian mathematics.  There are triangles and they are measured and there are angles, but none of the ratios we use today.  That comes later.  

Egyptians used symbols like people now use emoticons.  The Egyptians did not use emoticons.  

I think Greeks frequently get credit for everything, even when others find it first.  Ethnocentrism, if nothing else.  Also, Wikipedia is much less reliable as a source than our book (or than anything in print is, for that matter).  If you want to try a on-line source, please use the one I recommend on our website.  

For those who like etymologies, Suzuki will be a treat - the book is full of them.