Thursday, April 30, 2009

The Math Curse

Sue brought in this awesome kids book for math, The Math Curse. I was flipping through it. The illustrations are great and so is the story. The premise is a little girl starts to see everything as word problem. She's getting dressed, word problem. Oh, no! Riding the bus to school, word problem. She can't turn off the vision. That's the curse. Everything is math. If you have ever had to go to a party right after studying for your topology comps? You know exactly what she is going through.

Wednesday, April 29, 2009

Geek of the Week: Laura

Laura is our resident Foxtrot expert, which is a surprisingly geeky comic. You might remember the Fibonachos. That was Laura. Below is her latest find. I like this one even better. I can't wait to give it to my students.

I am also happy to report that the caché of the Geek of the Week award has risen, evidenced by the fact that people are now starting to prepare acceptance speeches. Here is an excerpt from the full 20 minute version of Laura's speech.
...Wow! Geek of the Week! I never thought I'd win! It was an honor just to be nominated...I'd like to thank the math department for selecting mom and dad for all their love and support and for giving me my first abacus and then my first slide rule...and let's not forget my Tunxis friends who love to remind me on a daily basis that I am a geek!

Tuesday, April 28, 2009

Correlation, Not Causation

This is another one for Sue's stat-heads. I grabbed it off Harvard's Social Science Statistics Blog. Somebody ought to stop the import of those lemons.

Monday, April 27, 2009

Mathematical Frenemies

This one came up on the problem widget (lower right) a while ago. I've been struggling with it.
A town creates a committee of six people to solve a new math problem. In the town, everyone is either a friend or an enemy. Prove that there are at least three friends or three enemies on the committee.
pic by Alana

Friday, April 24, 2009

Geek of the Week: Robert Devaney

Last Friday I attended the Spring MATYCONN meeting with my infamous colleague Sue. I was treated to a really excellent tour of the Mandelbrot set by BU prof Robert Devaney. Where most presentations of fractals seem to die in the pictoral realm, Devaney gave the necessary background to appreciate the pictures and inner patterns of the set. He also had some cool visualizations. He's got some of them posted on his homepage.

pic by Fermion

Thursday, April 23, 2009

Math Battle

If you've been reading along, you know I'm interested in finding a spectator friendly math competition. Kate left a provocative comment about the historical precedence of math battles on that post. I didn't run into any historical info, but when I googled 'math battle', I wound up with a Canadian group that has been running an interesting type of math competition it calls a math battle. What makes this more interesting than the usual paper and pencil test taken individually or in a group is that it is not graded. The answers are debated in front of a panel of judges and an audience. It starts in the normal manner with a problem set that each team works. Then the teams challenge each other's answers in a debate-style back and forth between the speakers. So not only can you score points by correctly solving the original problems, but you can also earn points by finding gaps or errors in your opponent's solution. I'm not sure this would work for us. I think John and Steve are thinking of something more immediate, physical, and faster moving, but I would love to see one of these competitions. It seems like an excellent idea. BTW, they also post their old problem sets so it is a great site to go to for a little mathematical recreation. I liked this one.
Two persons play a game on a board divided into 3 × 100 squares. They move in turn: the first places tiles of size 1 × 2 lengthwise (along the long axis of the board), the second, in the perpendicular direction. The loser is the one who cannot make a move. Which of the players can always win (no matter how his opponent plays), and what is the winning strategy?

pic by Bre!

Wednesday, April 22, 2009

Math and Makeup

This picture was sent in by a student for an enrichment assignment I give in Math for Liberal Arts. Here's the assignment.
Post to the discussion "A picture is worth..." your favorite graph, chart, diagram...etc. You can either attach an image file (.jpg or .gif), embed it, or give us a link. I also want the reason you like it. Could be what it says, could be visual organization/design.
This diagaram is from an independent makeup artist. Brittany Lewis. I am simultaneously drawn and repulsed by it. Who knew makeup could be so analytic? Very impressed.

Tuesday, April 21, 2009

Speed Pi

Rob sent this. Duly impressed.

Monday, April 20, 2009

New Tunxis Math Blog

Former Geek of the Week, Lee Bradley, has started a new math blog geared to helping students pass Tunxis's Intermediate Algebra exam. It's called CCPMath. I'm definitely sending my panic stricken students over to the blog after we get through test 3. Nice work, Lee!

Friday, April 17, 2009

Harmonic Mean

My wife is studying for an actuarial exam. She was doing an online seminar last night and I heard the speaker mention a harmonic mean. I hadn't ever heard of it, so I got curious. For three numbers a, b, and c. We know the average is (a+b+c)/3, but the harmonic mean is the reciprocal of the average of the reciprocals i.e. 3/(1/a+1/b+1/c). So for three particular numbers, 4, 7, and 8, the mean is 6 and 1/3. The harmonic mean is 5 and 23/29. I though cool, but when would I ever use this. Wikipedia gives an nice example:
What is the average speed of a car that goes a certain distance d at a speed of 60 kilometres per hour and then the same distance again at a speed of 40 kilometres per hour?
The (arithmetic) mean is of course 50. If we calculate the average speed directly, we wind up with a different number. The average speed is the distance they traveled divided by the time. The car travels 2d, and the time traveling at 60 kph is d/60. The time at 40 kph is d/40. So we have the average speed as 2d/(d/60+d/40). We simplify 2d/(5d/120) = 240d/5d = 48. This is what we would have go if we'd calculated the harmonic mean of the rates: 2/(1/60+1/40). Cool, huh? I found out there are other means, geometric and quadractic. I'd like to get examples for each of the others.

pic by mince

Thursday, April 16, 2009

Using xtimeline in class

Here is an interesting project my math for liberal arts class started. They used xtimeline to start a history of math timeline. We're a small class so there are only around 10 posts right now. I hope to grow this over the semesters. It was my first project like this. I waffled between using xtimeline and TimeToast. I liked TimeToast better visually, but it doesn't accept BC dates. That's fatal for a history of math timeline. xtimeline also allows multiple editors. The down sides are the appearance and the embed code is slow to load and akward. I'd like to hear in the comments of experience with similar net apps. I'm planning on doing my course schedule on one of these next semester.

Below is Jim R's Tunxis timeline. He tipped me off on this nice set of web tools. Thanks, Jim!

Wednesday, April 15, 2009

Semester Drag

It is that time of the semester when everyone is feeling a little bedraggled. My students are looking at me like if I ask them to simplify one more expression they will pass out. I try to put a good face on, but I'm feeling it too. In short, we're all a little fried. Soon the finals adrenaline rush will save us, but in the meantime I figured we all might need a reminder why we take/teach a math class. I found this graphic over at Filckr by Network Osaka. The graphic is really cool. Make sure to blow it up.

Tuesday, April 14, 2009

Statistically Significant Other

I thought Sue and her stat-heads would enjoy this one. It's an xkcd comic I ran into on Math Stories.

Monday, April 13, 2009

Bonus problem for College Algebra

I thought this might be a nice bonus problem for a college algebra class.

Let A be some number. If c = log(A) and c = a+b where a is a non-negative integer and b is a decimal between zero and one, represent A in scientific notation.

Maybe a concrete form of the question would be better for students: If log(A) = 4.182, approximate A in scientific notation.

Friday, April 10, 2009

Tunxis Math Contest Winners

I want to send out a congratulation to CK and Jeff who tied for first place in the Tunxis math contest. They are both $200 richer at the moment. Who said math will never bring you fame and fortune?

pic by Terren

Thursday, April 9, 2009

Mathematical Comedy

The Second City is comedy venue started in 1959 in Chicago. They now have branches in Toronto and LA. They have fostered the early careers of a lot of comedians (Bill Murray, the Belushi's, John Candy, Dan Aykroyd, Mike Myers...). Sourcebooks MediaFusion released a retrospective of all the great talent that came through SC. I haven't actually read the book, but it is accompanied by two Cd's that I absolutely love. They're filled with some of the best SC sketches. Here are a couple that tickled my mathematical funny bone.

(Warning: the comedy is a little rough. If you are sensitive or a younger reader, it is best to leave this post alone. There aren't any of the holy, holy swear words, but a few minor peccadilloes, and a lot of unpolitically correct humor. Remember, if you can't take a joke, don't.)

Ever feel like you belong to the null set? (Don't think too hard about that.)

And this is a doctors appointment on stats.

Wednesday, April 8, 2009

Geek of the Week: Bertrand Russell

My youngest reader Lia sent me this quote from Bertrand Russell for the blog.
There is much pleasure to be gained from useless knowledge.
It made me think of another great quote Jean-Marc introduced me to from Russell's autobiography. (BTW, Russell had a very unhappy youth.)
There was a footpath leading across fields to New Southgate, and I used to go there alone to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more mathematics.
It suggests that all anyone seriously depressed needs is a little more math. I'm not sure geometry is ready to replace Prozac, but if it worked for Russell, it's worth a shot.

I googled Russell quotes because I forgot the exact wording on Jean-Marc's quote, and I found out that Russell was a master of the form. QuotationsPage had 63 entries for Russell. Here are some good ones.
Everything is vague to a degree you do not realize till you have tried to make it precise.
This beautifully echoes the wonderful failure of his project Principia Mathematica.
If there were in the world today any large number of people who desired their own happiness more than they desired the unhappiness of others, we could have paradise in a few years.
I have to believe he's exaggerating for effect, but let's hear it for a little enlightened self-interest! I could go on forever, but I'll end on this one about teaching.
Passive acceptance of the teacher's wisdom is easy to most boys and girls. It involves no effort of independent thought, and seems rational because the teacher knows more than his pupils; it is moreover the way to win the favour of the teacher unless he is a very exceptional man. Yet the habit of passive acceptance is a disastrous one in later life. It causes man to seek and to accept a leader, and to accept as a leader whoever is established in that position.

pic by Gisela Giardino

Tuesday, April 7, 2009

Prime Time

I was thinking about the possibility of defining a subset of the naturals containing numbers whose digits (appropriately grouped) are its own prime factorization. For example, take 32. It would be a number of this kind if 32 = (3)(2). (Of course it's not.) Are there any members of this set? Well, every prime number is trivially a member, 7 = 7, 11 = 11. The interesting question is, does this set have any composite members? I haven't been able to think of one yet.

I quickly checked the numbers less than 100 and there aren't any examples there. The only single digit numbers in this set are the primes. Consider the double digit numbers, 10 through 19. Let A be a digit, 0 through 9, if 1A = (1)(A), then 1A = A. Since no two digit number is equivalent to a one digit number, this isn't possible. (Note, 1A does not mean 1*A.) What about the numbers 20-29? If 2A = (2)(A), then the most (2)(A) could be is 14, because the most A could be is 7. But we know 2A is in the 20's so this is not possible. Any number in the 30's, 50's, and 70's will have the same problem. Any number 4A can only be grouped (4A) because 4 is not prime. So only the boring numbers (primes) in the 40's make it into the set. Same is true for the 60's, 80's, and 90's. What can we conclude? There is no composite example less than 100.

What about 3 digit numbers? We can start to make arguments by thinking of the grouping possibilities. If ABC is a three digit number, then we could group (A)(B)(C), (AB)(C), (A)(BC). Your mission: find a composite number in this set, or prove that there aren't any.

pic by kingfal

Monday, April 6, 2009

Math Contest

Friday was a big day for math at Tunxis. Both the Pi contest and CCC system-wide math contest were going down. It was a great day. The victor of the pi contest, Alex Bobman, memorized a whopping 302 digits! We are still waiting for the results of the math contest, but I'll post those as soon as I find out.
I was also able to get a copy of the math contest problems. I thought I'd pass along something fun.

A farmer had a daughter who spoke in riddles. One day the child was asked to count the number of goats and the number of ducks in the barnyard. She returned and said, "Twice the number of heads is 76 less than the number of of legs." How many goats were in the barnyard?

pic by ADoseofShipBoy

Friday, April 3, 2009

Math and Dance

I have a friend who is getting her doctorate in dance. I asked her if she knew of any intersection between math and dance. She dug up this link to Mathdance. There are a couple of professors that have written a series of instructional dance activities to teach math concepts. Pretty wild. I can't ever imagine leading my students in a ensemble dance of irrational numbers. Maybe I should. I went looking for inspiration on Youtube and found the Dance of Parallel Lines...

and some kind of wild trig dance...

Thursday, April 2, 2009

Math, the Chaste Science

Check out this snarky math comic. Would anything outflank math on the right? Could there be a logician out there saying, mathematics is just applied logic?

Wednesday, April 1, 2009

Wine and Math

Who knew math would help you drink better? Enologix is a Napa Valley consultant using data analysis to help vineyards make better wine. I caught their profile in Wired. Not surprising in an industry dominated by connoisseurship, the analytic approach to production decisions has been quite controversial. I guess the only thing to do is open a bottle and find out. (You know the geeks are going to win, right. The geeks always win.)

pic by Buson