## Math Mistakes and Misplaced Measuring

March 14, 2012 by

In an unfortunately tribute to Pi Day and the importance of mathematics, there was an article in the New York Times yesterday (March 13, 2012) illustrating that the people who need to measure parts don’t always know how:

“The employee responsible for finding a replacement part for a tower crane that ultimately collapsed on the Upper East Side in 2008, killing two workers, testified on Tuesday about his own difficulty with the basic math of measuring key components. Tibor Varganyi, whose formal education ended in the ninth grade in Hungary, struggled how to measure the distance between the roughly 30 bolt holes around a piece of the turntable assembly. He decided to use a ruler.”

The article (“Worker Tells Court He Lacked Math to Measure Crane Part” by Russ Buettner)goes on to explain how the measurements didn’t match up with expectations, so he switched to a protractor, which also didn’t work.  This particular replacement part was never used, and the article is primarily about the prosecution’s argument that the company wasn’t worried about the lack of expertise or safety, instead focusing on profits, but the description is still worrisome.

That’s depressing.  We’d better recover by looking back at some old Pi Day Sudokus.

## Happy Birthday Jim!

September 24, 2011 by

As you’ll know if  you’ve been on Google in the past twelve or so hours, today is Jim Henson’s 75th birthday, and in his honor we share with you a rousing rendition of the How Many Game, hosted by the wonderful Guy Smiley!

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.

## How many before the end?

September 20, 2011 by

Let’s start with ultimate (yes, that seems a bit backwards – stay with me.), as in “last”.  The next-to-last, then, is penultimate, easily one of my favorite words.  But there’s more!  The next-to-next-to-last is the antepenultimate.  Need another?  The $(\text{next-to})^3$-last is the preantepenultimate, a completely real word that Chrome’s built-in dictionary has never seen (it suggests “prearrangement”).

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:

## Granola Fail

August 24, 2011 by

From a recent Nature Valley ad in the London Metro newspaper:

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

Via Language Log.  Photo from Spiderham.

## Math Neglect on Glee

April 22, 2011 by

The folk from Glee paid unintended homage to the title of this week’s episode (“A Night of Neglect”) by showing Mr. Schuester forgetting his basic math skills.  Actually that’s not entirely true; he does math in his head correctly as he explains his plan to use salt-water taffy to earn money to go to Nationals in New York:

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.

## Alpha’s Curious Filter

April 19, 2011 by

For no reason that I can think of, I decided to see how much Wolfram Alpha knew about probability, so I typed “probability of a full house” into the search box and got the following:

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 $\binom{52}{5}$.  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.

April 12, 2011 by

Godzilla is a well-known mind-reader, and in honor of final exams, which are coming up sooner than seems possible, he’d like to demonstrate his powers.  Even over the internet, because his powers are MIGHTY.  Like him.

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…..

## The Carnival Lives!

April 10, 2011 by

The Carnival of Mathematics is still going strong.  This round – #76 – is hosted over at Walking Randomly and has, as usual, something for everyone, including a post from one my favorites: Language Log.  (Yes, they use math there.  Fairly often, in fact.)  Go check it out, and while you’re at it, contact Mike if you’d like to host one.

## The Difference

April 9, 2011 by

Friday’s Saturday Morning Breakfast Cereal.  (Click to view the original along with the bonus content.)

So which are you?

## Time to Fail!

April 8, 2011 by

We luv us some failblog (regular or decaf), particularly on a Friday.   Lately they’ve had a bunch of math fails, where “lately” means “since the last time we posted from there” and “bunch” is closer in number to “I bought a bunch of bananas” than “I have a bunch of papers to grade”.  So without further ado, here are some favorites.

There’s trouble with dates:

and trouble with money:

and lots of trouble with percents:

Apparently, as Barbie once said, math is hard.

## Twelves

April 6, 2011 by

The number 1729 has a right to be proud :  it initially had only a small role on a taxicab in England but its super-power of being the sum of  two positive cubes in not one but two ways (13+123 and 93+103) led to a big break in a Feature Story starring GH Hardy and Srinivasa Ramanujan, with follow-up appearances for years to come on the likes of Futurama and Proof.  So, you know, yay 1729.

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.

## Illusion Knitting

April 4, 2011 by

See Mini-G look at this fine piece of stripey art:

Isn’t that interesting, full of nuance?  NO — it looks totally boring.  But Mini-G is actually looking at it at an angle, which turns out to be a completely different story.

No more simple stripes!  And while it’s no Mona Lisa*, it’s pretty cool to see the shapes appear just as you start to walk away in search of something less vertical to look at.  Even better, it’s simple knitting.  REALLY simple knitting, just knits and purls, where using stockinette stitch makes a color fade into the background when viewed from the side, and using garter stitch makes a color stand out.  There’s a great explanation here, where “great”=“uses legos”.

This comes from Woolly Thoughts (“In pursuit of Crafty Mathematics”) and their newish illusion site.  It’s a free pattern — Woo hoo! — and not that I’m suggesting that you knit during meetings or anything, but if you DID knit during meetings this particular pattern is simple enough that you can do it without being distracted from the Important Conversations and Presentations, and then you can feel good at the end of two hours that you made quite a bit of progress on your knitting whether the meeting led to a resolution or not, plus you get to point out that you’re really doing mathematics if anyone asks what you’re knitting.  Win-win!

* though there is a pattern for that.

April 3, 2011 by

The forecast this moment is predicting snow…SNOW!…and while it’s not going to be much, it looks like winter won’t end until we post our Winter Newsletter.  This issue is named The Chern Weekly Quarterly Whenever after Shiing-shen Chern (陳省身, Oct. 26, 1911—Dec. 3, 2004), who studied Differential Geometry (including, ummm, Chern classes in algebraic topology), was vice-president of the American Mathematical Society, and who founded the Mathematical Sciences Research Institute at Berkeley and the Nankai Institute for Mathematics.

This issue contains mostly department news and photos, but as always it contains a Sudoku and problems for your mathematical enjoyment!

Problem 5.2.1: Find the ratio of the areas of the circumcircles of a triangle and a square of equal perimeters.

Problem 5.2.2: In the figure at the right, ABCD is a rectangle, BE=BC, and AE is the diameter of the circle. What is relationship between BF and the original rectangle?

Problem 5.2.3: Using the digits 1-9 exactly once each, with only the operations +, —, ×, ÷, and/or exponentiation, write an expression that equals 2011. Now try it with the digits in order.

Problem 5.2.4: A box has three possible perimeters. Suppose box A has perimeters 12, 16, and 20, while box B has perimeters 12, 16, and 24. Which box has the greater volume?

You’re welcome to try your hand at these and post in the comments, for fame (of sorts, although referring to it as “famish” doesn’t make it sound very enticing at all) since we’ll happily acknowledge all who submit solutions in the next issue!  Which isn’t as much of a temptation as just solving for solving’s sake, but still, we do what we can.

## If it’s Pi Day, that means…

March 14, 2011 by

Brainfreeze Puzzles must have a new Pi Day Puzzle up — woo hoo!!!!!

The Rules are to fill in this pie-shaped circle so that the numbers 1 through 12 appear:

• exactly once in each double-wedge of the same color,
• exactly once in each pair of opposite wedges, and
• exactly once in each ring around the center.

As in previous years, they are having a contest for correct entries (information on this website and this pdf file), so no hints or solutions are to be posted in the comments until the contest closes on June 1.  [If/when they print a solution, we’ll post a link to it.]

If you missed Brainfreeze’s earlier puzzles, here are the ones from:

## It’s a Threeven Day!

March 3, 2011 by

Happy 3/3 everyone!

I just graded a bunch of proofs that √3 is irrational.  The proofs had a lot of holes in them.  This didn’t surprise me too much, in large part because the students weren’t math majors; rather, it was for a liberal arts math class taken largely as a gen ed requirement, and the whole proof by contradiction thing is really pretty scary and abstract for most people the first time around under the best of circumstances.

But actually, even when I’ve assigned this to math majors, they struggle.  They can have the proof that √2 is irrational right in front of them, be instructed that instead of even numbers they want to look at multiples of 3, and despite my Find and Replace instructions, they still don’t understand what to do.  The most common mistake is to replace “even” with “odd”.

In some ways this doesn’t surprise me, but in some ways it does.  Why is it such a conceptual leap to go from 2 to 3?  It’s a HUGE leap for many people.  And so I was pondering this while grading, and Batman suggested it might be because we have a special word for “divisible by 2” but don’t for “divisible by 3”.  So you get, what, 10 years of reinforcement that there is just this one special way to divide the integers, and it doesn’t generalize.

What we need is a new word for these numbers.

And fortunately we have one:  threeven.  So 0, ±3, ±6, ±9, …  are all threeven, and the rest are…umm, not.  (Maybe we need two new words).  This word isn’t mine or even Batman’s; it actually was suggested by one of his students in response to this exact same problem.

As a bonus, it generalizes:  there’s fourven, fiven, sixen, seven-en (sev-en? )…as far as you want.     Which, admittedly, might not be very far but it still makes for a smoother sounding proof.

Happy threeven day!