Follow up question:  should they have won with the sheep?

According to the Muppet Wiki, Guy Smiley’s enthusiasm was rough on Jim Henson’s voicebox, so his portions were rerecorded so that it could be played over and over without Mr. Henson having to keep repeating his dialogue.   The Muppet Wiki also says that there were two two-headed monsters:  the one in the clip above was designed by Jim Henson, but a second, who was on Fanfare and the Mike Douglas Show rather than Sesame Street, was performed by Jim Henson.

Why am I telling you all this?  I mean, besides the sheer ridiculousness/awesomeness of a word for the fourth-to-last item in a list?  I needed an excuse to post this video:

Perhaps the second bar is twice as delicious as the first.

Via Language Log.  Photo from Spiderham.

When I was a student here we paid for our entire trip to Nationals selling this….  So, to make $5000 at 25 cents apiece, we need to sell 20,000 pieces of taffy.

So far, so good.  But wait, what’s that equation in the background?

Poor Will…he didn’t even notice that the equation wasn’t quite right (and neither did the four members of the Academic Decathalon team).  But don’t worry, we understand how busy this time of year is, what with all the projects and end of the year assignments coming due.  So shall we just fix that up for you?

There, all better.   Now you can go concentrate on raising that money.  Just be sure to have someone else in charge of the ledger.

I thought that was pretty cool, especially since it includes the derivations, so I asked a few more questions, such as “probability of at least 2 red cards in a 5 card hand“:

Odd that it will count the numerator but not the (easier) denominator .  At this point, I thought I’d try a standard probability question (balls in an urn) that might be harder to parse because of the additional statements: “probability of drawing a blue ball from an urn contaiing 5 blue balls and 7 red balls“.  However, I missed the ‘n’ key when typing “containing” and got the following:

So, yeah, OK, Wolfram Alpha doesn’t provide “adult” content (why the quotes?), and I’m pretty sure I know what it’s reading as “adult”, but c’mon.  Note that fixing the typo doesn’t alleviate the problem, but it does cause Alpha to hiccup and request more computing time.  With variations on the wording, I’ve also had it return a picture of a blue ball along with the HTML code to generate it.  Nice.

Start with 3-digit number that is not a palindrome (so 360 is OK, but 363 is not).    Then reverse the digits, and subtract the smaller number from the larger.  You get a NEW AND IMPROVED number.  So if you do start with 360, your NEW AND IMPROVED number will be 297 (which is 360 minus 063).

Treating your NEW AND IMPROVED number as a 3-digit number, reverse the digits.   This means that if your NEW AND IMPROVED number appeared to only have two digits, or even one, then you have to tack on one or two leading zeros that you include in the reversal.

Now add your NEW AND IMPROVED number to its reverse.  Godzilla will now tell you the sum, even over all the miles and electrons that separate you from this friendly beast…..

Poor 1089 doesn’t look like it’s having a very good day.  But he’ll be the star of the show if you do this trick yourself, with super mindreading powers passed along by the Big Lizard himself.

If you want to avoid the whole “leading zero” thing, you can insist that the first and third digits of your starting number are at least two digits apart, which sounds unduly complicated, or that the digits are all increasing [or all decreasing], which sounds slick.  It’s not really necessary, though.

Hat tip to Michaela Stone and Michelle Zajac from Alfred University:  they didn’t invent this trick, but they did share it in a talk at the MAA Seaway Conference at Naz earlier this month.

So which are you?

There’s trouble with dates:

and trouble with money:

and lots of trouble with percents:

Apparently, as Barbie once said, math is hard.

But lest this Hardy-Ramanjuan number get too boastful, it’s not the only sequin at the Oscars.  Its neighbor, that unassuming 1728, turns out to be an interesting character in its own right.

The origin of this is in the dozen.  Although ten is a pretty natural base to use, in the sense that a lot of cultures break numbers up by tens in some form, it’s not the only possibility.   We have not only a special word for 12 (dozen), but a special word for 12² (gross), which suggests that our language carries hints of a Base 12 system.  And that leads to the question:  is there a special name for 12³?

There is!  The official name is a Great Gross.   And while dozen and gross show up in egg cartons, it’s in measurement that the great gross really shines:  there are a dozen inches in a foot, a gross square inches in a square foot, and a great gross cubic inches in a cubic foot.

But while the great gross is helping out with set design, there’s a rumor (which we’re apparently happy to help spread) that 1728 actually has a stage name.  That’s because there’s a theorem about L-functions of elliptic curves called the Gross-Zagier Theorem, named after Benedict Gross and Don Zagier.  So the natural extension of a gross is…a Zagier!  Or at least that’s the name that 1728 goes by on the cocktail circuit according to Wikipedia, our local gossip rag.  Which makes us wonder where this down-to-earth yet whimsical number will show up next.

In an amusing turn of events, it turns out that Gross and Zagier won the Frank Nelson Cole prize in Number Theory in 1987 from the American Mathematical Society for their paper “Heegner points and derivatives of L-series” which contained the above theorem.  The other winner that year for a different paper was Dorian M. Goldfeld who, the following year, published a paper with M. Anshel entitled “Applications of the Hardy-Ramanujan partition theory to linear diophantine problems,” bringing it all back full-circles to the people who made 1729 famous.   It’s like one giant family reunion.