Archive for September, 2009

Carnivals Galore! Plus some Excel.

September 30, 2009

clown at the carnivalFirst off, there was a Math Teachers at Play (the second #15) just about two weeks ago.  It’s hosted by Maria Droujkova of the Math 2.0 Interest Group.    There’s the usual assortment of great stuff, including a computer game that I really want to play, and some stuff on Wolfram Alpha (which I know is totally old hat, but I gave two of my classes the homework assignment to play on W|A for 20 minutes and email me the neatest thing they found, and I think that’s been their favorite assignment so far.  Plus one of my Math for Liberal Arts groups cited it in a project when a pattern of numbers got too big for their calculator.  I love Wolfram Alpha) and sites for special needs students.

So that’s one carnival.

And the next is the Carnival of Mathematics #58 at Walking Randomly, up this past weekend, with near integers and binary in baby toys and maps.  (And now the 9-year old is wondering why I’m listening to  Men at Work).   Even though it’s not in the Carnival, also check out the post about (-1)*(-1)=+1.]

This has nothing to do with the Carnivals, but do you want to know what I learned how to do on Excel this weekend?  Conditional formatting!  I use Excel for my gradebook and I usually highlight if a student gets below 70% on exams or projects.  In the past I’ve done this by hand — which isn’t too time consuming because we’re not talking loads and loads of people — but it turns out that you can highlight a group of cells, go to Format, and then Conditional Formatting, and then set it up.  I even got lazy and for a 32-point assignment I set it to highlight scores less than “=70%*32”.    I expect this isn’t news to many people, but since the first person I mentioned it to hadn’t heard of it, I figure that’s good enough reason to bring it up.  Thanks for showing me this Nicole!

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Information Gain in “Manager-Speak”

September 28, 2009

There’s a neat post over at Language Log on determining whether or not someone is a manager if they say, “at the end of the day.”  It is the latest in a recent thread (parts 1, 2, 3) about irritating phrases being associated (often incorrectly) with irritating people (see here for an earlier discussion).

DIY Beanbags, or Tiling a Sphere

September 23, 2009

As an avid juggler, I have a rather large supply of props to juggle, most of which are balls or beanbags.  (Also on the shelves: clubs, rings, scarves, devil sticks, and a diabolo.)  As anyone who’s ever bought juggling equipment can tell you, this stuff isn’t cheap: decent beanbags can run $10-15 apiece, and rings and clubs are much more expensive.  So when I discovered these instructions to make your own beanbags, I was understandably excited.  (Of course, I’ll have to ask Batwoman to sew the pieces together for me.  Needles have a tendency to end up stuck in me instead of the fabric.)

Then I started clicking around the IJDb, and I found these.  Marylis Ramos has clearly spent a lot of time thinking about tiling a sphere.  Certainly any Platonic or Archimedean solid can be adapted to a sewing pattern to approximate a sphere, but a great deal of experimentation among jugglers and sewers has led to only a few becoming popular: the tetrahedron, cube, dodecahedron, icosahedron (one of the best, but really hard to sew), truncated tetrahedron, cuboctahedron, and the “lemon” (with 3, 4, 5, 6, or 8 panels).

spherical tetrahedronspherical cubespherical dodecahedron

spherical icosahedronspherical truncated tetrahedronspherical cuboctahedron

The pictures are, of course, idealized beanbags with perfect 1-dimensional seams that cannot be achieved by terrestrial sewing machines (at least not the Singer in my basement).  Or maybe they’re just from Wikipedia’s spherical polyhedron page.

I’ll be making some 4-panel lemons, and I’ll post a follow-up to discuss their sphericity (or lack thereof).

Math on Craigslist. Or not.

September 17, 2009

julia_setMichael over at God Plays Dice had a post in August that referenced the site You Suck at Craigslist, a blog with daily posts that feature real Craigslist ads that are too funny not to mock.  And it has turned into a fabulous time waster, not just for us but for all our students who are now addicted to the site  (Thanks Michael!)

But here’s the best part:  it features math on a regular basis.  For example:

But wait, there’s more!

So reading this is almost…almost…like studying.
Almost.

As it happens, the author, drmk, has a day job as a university professor Somewhere.

Carnival of Mathematics #57

September 11, 2009

Carnival of Mathematics Logo

Welcome to the 57th Carnival of Mathematics!  This particular carnival is sponsored by the numbers 57 and 2:  the first for the obvious reason and the second because it turned out that each contributor has two blog posts (though in some cases that will come as a surprise to the contributors).

The number 57, while not actually prime, is known as a Grothendieck prime in honor of Alexandre Grothendieck.  According to legend:

In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

This story is not implausible, because Grothendieck didn’t normally think in terms of numbers and actual examples (according to the rest of the article above).  Indeed, abstractness was a characteristic of his.  Speaking of characteristics, Akhil Mathews at fellow group blog Delta Epsilons has a post on Hensel’s lemma and a classification theorem for complete Discrete Valuation Rings with a residue field of characteristic zero.  (It’s actually part of a longer series, which I think starts here and continues over the next few days.)

The number 57 also occurs in the ketchup Heinz 57.  When they introduced their catsup, they had roughly 60 products of various sorts on the market.  57 sounded nice, so they called the catchup their 57th product.  In this case, they were just using the numbers to count, but another thing that you can do with numbers is to combine and permute them.  However, as John D. Cook shares over at The Endeavor,  a misunderstanding of those processes can (almost) lead to blows:  see Classroom Violence, Combinations, and Permutations for the full story. He also write about Gilbreath’s conjecture in Easy to Guess, Hard to Prove, which provides a great example to share with students about a math problem that seems simple but, as the title suggests, isn’t.

Rod Carvalho wrote two posts on optimal debt allocation over at Reasonable Deviations:   Part I is here and Part II is here.  The articles, inspired by real-life bill-splitting at dinner, pose some interesting questions that I hope are solved soon.  Something else that is solved — well, really, solvable — is any group of order 57.  (There are several reasons for this, the simplest being that 57 is the product of two odd primes.)

Both TwoPi and I started our life in California, which has 58 counties.  (Yes, that’s not 57.  No state has 57 counties, though Montana would win the Price is Right prize with 56).  Speaking of life, Nathaniel Johnston shares a post on generating sequences of primes in Conway’s game of life .  Also check out today’s post about how primes with millions of digits aren’t useful for cryptography.

And last but not least, Pat Ballew of Pat’sBlog wrote about samuri and mathematics in Pi and the 47 Ronin, with a request for any photos that might be available of the tomb of Matsumura.    He also explored an exploration by Leibniz in Limits as x→Infinity.  Something that isn’t infinite is the list of Idoneal numbers:

An idoneal number, also called a suitable number or convenient number, is a positive integer D such that any integer expressible in only one way as x^2\pm Dy^2 (where x2 is relatively prime to Dy2) is a prime, prime power, or twice one of these.

There are only 65 of them, or maybe 66 if the generalized Riemann hypothesis holds.  The number 57 is one of those Idoneal numbers.  Isn’t that Convenient?

The next Carnival of Mathematics will be hosted by Michael Croucher over at Walking Randomly!  See you there in two weeks!

Recent MTaP #15 and Upcoming Carnival of Math #57

September 8, 2009

The most recent Math Teachers at Play, #15, is up at the Homeschool Math Blog.  I got completely distracted by the first post about some math for kindergarteners, and several clicks later I was listening to binary music.  As usual the rest of the Carnival is full of great stuff as well.

Speaking of Carnivals, assuming I don’t lose track of the days we’re hosting the next Carnival of Mathematics here on Friday!  You can email submissions to hlewis5#naz.edu [except replace that # with a @], ideally putting something like “Carnival” in the title, or post a link here or with the previous announcement.  And since I’m a procrastinator, I’d say you safely have through Thursday night to submit.

On an unrelated note, but just because it’s fun, here’s what a colleague wrote on the whiteboard of my office:

111,111,111×111,111,111

(I think it’s more fun to do by hand than on a calculator, but it’s neat however you find the answer.)

Multi-untasking

September 3, 2009

User-ASE-BusyLast week I ran across an article by Randolph E. Schmid that, judging from the google search I just did, made its way all around the networks [here it is at the Huffington Post] but I still find fascinating.  People who multitask don’t do it very well.

The article describes how they tested this, and below is one of my favorite quotes, in which study-guy Clifford Nass described the outcome of one of the experiments  in which the participants looked at red and blue rectangles [that’s the Math part of this post] and then had to determine if the red ones had moved, ignoring anything about the blue rectangles.  They thought high multitaskers would be good at this:

But they’re not. They’re worse. They’re much worse….They couldn’t ignore stuff that doesn’t matter. They love stuff that doesn’t matter.

(I love that last line.)

In other tests the high multitaskers couldn’t organize information as well as others, and were the same as far as memory goes.  In the last test people had to identify letters and vowels or consonants and numbers as even or odd [that’s the Bonus Math part of this post], but it turns out that high multitaskers had a lot of trouble switching between the two tasks, despite what one would think is constant practice of changing focus.

I’m not sure what to do with this information, and no doubt it needs further study yadda yadda yadda.  But I found the concept fascinating as far as teaching goes, and I’m still left wondering what high multitaskers are good at.  Maybe nothing, but I believe deep down inside that multitasking must provide some skills.  Or maybe I’m just hoping.

Amazon isn’t Transitive

September 2, 2009

transitive2You know on Amazon.com how, when you’re looking at an item, at the bottom it will sometimes suggest combinations?  Usually I just see one suggestion, but sometimes there are two:

transitive

Really?  These are frequently bought together?  I can believe that bed pillows and lap desks are often bought together (at least, more often than other combinations) but even if the tan pillow is often bought with a lap desk, and a lap desk is often bought with the pink shag pillow, it doesn’t follow that customers often buy tan and muppet-pink bed pillows together, in the same shipment, even for the Super Saver discount.  It’s an odd combination, though surpassed by a similar triple that I found but didn’t think to save and couldn’t recreate:  a home theater system that is “Frequently Bought Together” with HDMI cords and another complete home theater system.  Perhaps to encourage you to have a backup at the ready in case you don’t like the first.

The photo in the upper left is actually another strange combination, but not about transitivity:  one brand of lap desk is purportedly frequently bought with a different brand of lap desk.  I guess this demonstrates that the Frequently Boughts, while not reflexive, is also not anti-reflexive.