Archive for May, 2009

The Actual Dresden Codex

May 5, 2009

dresden_codex_p09Happy Cinco de Mayo!    A year ago we celebrated the day here by talking about some Cinco de May math, branching out into Spanish Colonial Mathematics [including a really cool multiplication technique called The Method of the Cup].

But that was a pretty broad geographical region, so today it’s back to Mexico, with Guatemala, Belize, and maybe a little bit of Honduras and El Salvador thrown in.  (Aside:  I often make students learn where countries are when I teach The History of Mathematics, and a few times I’ve had them memorize all the countries of Central America for the first test.   One year I had the great idea that I’d test them on a map with no political boundaries, reasoning that there is some value in being able to identify countries by other landmarks.   Although I’d warned them about this, it turned out to be a truly awful test to grade — some people started off wrong, so while the countries were right in relation to each other they were all either too far north or too far south, and figuring out partial credit was a bear. I’ve never given a test like that again.)

So anyway, here’s the region we’re talking about:

Yep, it’s the Mayas!  I’ve seen a lot of math books that talk about Mayan mathematics, because it’s pretty straightforward (until it isn’t).

A dot means 1:  •
A line means 5:  ______
And a shell means zero.

The Mayans used a modified Base 20 system, so that the group of numbers at the bottom counted the 1s, the next group up counted the 20s, the next group up counted the 360s [and yes, it should really be 400 because twenty 20s is 400, but for some reason they used 360 here.  I’ve seen speculation as to why — it might have something to do with the fact that there are just over 360 days in a year — but no one knows for sure], the next group up counted the 7200 [because that is twenty 360s], the next group up counted the 144000 [because that is twenty 7200s], etc.

But the point of this post is that because the Internet is such an amazing place, you can see images of the actual original sources that use this!  Sadly, there aren’t that many:  most of the writings were destroyed, and only about four codices remain.  Codices are folded books, like this one (from the St. Andrew’s web site).

This is the Dresden Codex, and it’s about a thousand years old.  It was made of Amatl paper [fig bark covered with a lime paste], and although the picture above is in black and white it was actually done in color.  Indeed, when it came to numbers the groups (1, 20s, 360s, etc) were written in alternating black and red so that it was easy to tell where one group ended and other began.

dresden_codex_annotated1Look at that number in the lower left-hand corner.   There are 7 (1s), then 1 (20), 4 (360s), 6 (7,200s), 3 (144,000s), 11 (2,880,000), 3 (57,600,000s), and 6 (1,152,000,000s), giving a sum of over 7 billion.  It’s a pretty big number, and only uses 2 symbols [since the zero wasn’t  necessary in this case].

When I started teaching about Mayan numbers, there weren’t many pictures of the Dresden Codex available so I made do with a photocopy of the one of the pages.  But the Internet is an amazing place, and now you can actually see the entire thing in color in not one but two places!

The first place I found it is this site (archaeoastronomie).  It has the best pictures; my favorite for looking at numbers is page 51 and the pages around it [the zooming is really impressive, although it doesn’t necessarily zoom to the page you want].

And more recently there’s the Foundation for Advancemet of Mesoamerican Studies, Inc. They also provide downloadable .pdf files here [on the order of 100 Mb, but the download page offers the option of downloading in sections].  Hooray for the Internet!


More Big Bills

May 4, 2009

Yesterday I posted about the biggest bills in the US, and that was interesting to me in a historical sense.  However, the part of me that likes big numbers really liked seeing what other countries had to offer.

This proved to be difficult.  There are a lot of countries, and even individual countries change their currencies from time to time, especially if there is high inflation [which would be tied to really big numbers on the bills].  Here is but a small sample.

There’s a 100,000 rubles bill (2000) from Belarus, worth about US$36.

There used to be a 2,000,000 złotych (1992) in Poland but in 1995 the złoty was formed by dropping 4 of the zeroes, leaving the largest current note as 200 złoty.  It’s worth about US$61 and has Ignacy Jan Paderewski on the front, who was a Prime Minster of Poland and also a world-class pianist.

From 1990-2005 there was a 20,000,000 note in Turkish Lira.  Isn’t it colorful?  It’s got Mustafa Kemal Atatürk on it.  He was the first president of Turkey, and in 1927 gave a speech that lasted 36 hours.

But the numbers don’t stop in the millions, no siree.  About 15 years ago Yugoslavia, right before it split up, had a  500 billion dinar note featuring Serbian poet Jovan Jovanović Zmaj:

From the National Bank of Serbia (NBS Copyright)

And that’s not even the biggest.  Zimbabwe is still undergoing hyperinflation, and has a 100 billion dollar bill (2008):

Even with all those zeroes it’s not worth much, less than US$1, and by the time you read this the value will have decreased even more.   Less than four months ago newspapers reported that Zimbabwe would start printing notes in the trillions, up to and including a 100,000,000,000,000 dollar note, worth about US$30 at the time.

Big Bills in the US

May 3, 2009

100000-cornerAfter reading Denise’s post on large amounts of money, I started to wonder what the largest bill in circulation is.    I started with the US.

The largest bill I knew of was the $100 bill.   Ben Franklin invented the carriage odometer.

$100 bill.  Ben Franklin invented the carriage odometer.

I figured there were a few bills above that, getting into the $1000s, but it turns out that this is the largest denomination in circulation in the US.

There used to be a $500 bill.   A 1918 version had John Marshall on it, but the 1928 and 1934 runs had William McKinley.  The man who shot William McKinley was executed in Auburn, not far from here.

$500 bill.  The man who shot William McKinley was executed in Auburn, not far from here.

And there used to be a $1000 bill, in 1918 with Alexander Hamilton and in 1928 with Grover Cleveland.  We have two cards for Grover Cleveland in our Deck of US Presidents since he served non-consecutive terms.

$1000 bill.  We have two cards for Grover Cleveland in our Deck of US Presidents since he served non-consecutive terms.

There’s a $5000 bill with James Madison.  His wife’s sister’s husband’s uncle was George Washington.

$5000 bill.  James Madison's wife's sister's husband's uncle was George Washington.

There’s even a $10,000 bill with Salmon Portland Chase.  He was Secretary of the Treasury in 1862 when the first bills were printed and he put his own picture on some early bills although this one was designed after he died.

$10,000 bill.  Salmon Portland Chase designed money, and he put his own face on early bills although this one was designed after he died.

That’s it for bills, although there was a $100,000 gold certificate with Woodrow Wilson.  In 1915 Woodrow Wilson became the first sitting president to go to a World Series baseball game; a year later he thew the opening ball.

$100,000 bill.  In 1915 Woodrow Wilson became the first sitting president to go to a World Series baseball game; a year later he thew the opening ball.

“So what happened to all that fine money?” you may be wondering.  Well, bills just weren’t all that popular.  OK, I’m sure they were popular in the  sense that no one would turn them down, but there weren’t a lot of them in circulation.    The $100,000 bill [with a buying power today over over $1.5 million] was never in public circulation — it was only for Official Transactions between Federal Reserve Banks [and apparently it’s illegal to for collectors to even have one], and the others haven’t been printed in more than 60 years.  Indeed, in 1969 the Federal Reserve said something along the lines of “Enough of this” and discontinued them.  I think that means that they stopped giving them out as change, although they’re still officially legal tender so those of you who have them in your wallet are still OK.

Math Teachers at Play #6 [and bonus comics!]

May 1, 2009

Daffodils and TulipsHappy May Day!  And not only is it May Day, but it’s a Carnival Day!  Math Teachers at Play #6 is up over at I Want to Teach Forever, the blog of high school teacher Mr. D in Boston.   It’s a little shorter than previous ones, but no less valuable and a fine read on this Spring/Autumn day [depending on your hemisphere, of course].

On a completely unrelated note, recently I noticed people looking for the comic Nearing-Zero, which we posted on a year ago.  I did some exploring, and the comic has now changed its domain and is living here.

Speaking of comics, do any of you read Dinosaur Comics?  They have some math ones from time to time, so there’s a tangential relation to this blog, but this one last week, though not math-related, was one of my favorites.  (Click on the comic for an easier-to-read version.)

here is where i admit to spending the entire time writing this comic with all my kid icarus theme song remixes and covers playing on loop! nicolas ferranti, yours is my favourite.