Tuesday, June 30, 2009

A Mathematician Goes on Vacation 4

I saw this symbol on a lot of walls. It is the Serbian Cross. I'm told the meaning is basically equivalent to our motto "United We Stand, Divided We Fall" (although the Wikipedia article says that this interpretation is a common misconception). I was impressed by the interesting symmetry: two lines of reflection and rotational symmetry.

pic by alexmac1

Monday, June 29, 2009

Amoeba Fever Problem

Here's a very interesting problem sent in by Lee. Have fun playing with this.
Toby has a jar with one amoeba in it. Every minute, every amoeba turns into 0, 1, 2, or 3 amoebae with a probability of 1/4 for each case (dies, does nothing, splits into two, or splits into three). What is the probability that the amoeba population eventually dies out?
If you're wondering, Lee's brother Chip created the image above. I'm guessing it has something to do with the solution.

Friday, June 26, 2009

A Mathematician Goes on Vacation 3

As I said the first week it rained...a lot. That wasn't all bad. I did get a chance to read a bit. I brought along On Aggression by Konrad Lorenz. I'm not much of a biologist so a lot of the animal behavior descriptions flew over my head. But, I felt right at home with the above diagram. How nice to find a Caley table in the middle of a ten page meditation on the nuances of the duck and drake mating ceremony! Remember your multiplication tables? This is a binary operation. A binary of operation of what? Lorenz call the above diagram a motivational analysis Each picture on the diagram is a combination of the dog's fight or flight instincts. If you go down the left most column, you are seeing the progression of the flight instinct. Going across the top most row, you are getting the progression of the fight instinct. Any other image is some combination of the two instincts. All part of the math of mother nature. Quite interesting!

Thursday, June 25, 2009

A Mathematician Goes on Vacation 2

So, I didn't have such good luck with weather. It rained the whole first week I was there, which meant I watched a lot of Serbian TV on my inlaws' couch. Thank goodness The French Open was on Eurosport or I would have lost my mind. I also caught the above video quite a lot. (Their national stations play music videos between programs.) It seems to be the summer dance jam. There actually is some math in it, and if you can see it betwixt all the half-naked dancers, you know you're a bona fide geek. Good luck!

Wednesday, June 24, 2009

A Mathematician Goes on Vacation 1

I just got back from a three week visit of my wife's family in Serbia. I was on the lookout for anything mathematical. Check out this equation on the 100 dinar note (about $1.55). The mug is Nikola Tesla's. He is a Serbian national hero for his contributions to electrical engineering. The equation calculates a unit of measure the tesla which measures magnetic flux density. I tried to figure out what this means. No luck. (It did remind me of the flux capacitor though.)

Tuesday, June 23, 2009

Mathematical Fortune

I thought all the statbots out there would get a kick out of this fortune.

Monday, June 22, 2009

Math Donkeys

I love to give this problem to students.
Two Donkeys are walking down the road loaded down with sacks of potatoes. One looks over at the other and says, "hey, if you give me a sack, I'll have twice as many as you; and if I give you one we'll have the same number. Weird, huh?" The other donkey just says, "Geek" and keeps walking. How many potato sacks does each donkey have?
pic by kaysare

Friday, June 19, 2009

Beatles Mystery Chord Found...by a mathematician

This is a great story found on Scientific Blogging. The opening chord to the Beatles' song Hard Days Night had long stumped musicians and musical historians. It took a mathematician, Jason Brown, using a Fourier Transform to decompose the chord into its original frequencies. Was it George's 12 string, John's 6 string, or Paul's bass? Find out what the missing ingredient was.

Thursday, June 18, 2009

Tweaking Life

This is a thought on the game of life that Lee introduced me to a while back. John Conway has said that he played around with various rules to see which would produce the most interesting results. I took him to mean that he played around with the survival and birth rules. I was wondering if anyone has played around with tiles having different iteration speeds? Consider if every other column iterated at twice the speed. Basically squares could "play" at different speeds. Has anyone seen anything like this? Lee? Ken, I know you said you've played around with cellular automata?

Wednesday, June 17, 2009

Geek of the Week: Nerd Nook

I've seen a lot of math t-shirts. This one on Nerd Nook's photostream caught my attention. (might have to blow it up to read it.) In the 18 million times I've been asked, 'When will I ever use this in the real world?', I have yet to use this technique. It's kind of Dirty Harry meets underpaid math teacher. He also has a bunch of other t-shirts. I love this one.

Tuesday, June 16, 2009

Mystery Equation

I was struck by this illustration browsing Drawn's feed. I still haven't figured out what the equation is supposed to relate. The caption on illustrator Mark Smith's site reads
Green idealists fail to make the grade. The people that recycle the most are also the most likely to cause serious environmental damage by taking long haul flights when holidaying abroad.
Is the equation relating atmospheric quantities? Any of you know? Check out Smith's other work. You might enjoy it as much as I did.

Monday, June 15, 2009

Breakout Sessions?

I remember being at the Barnes Seminar last year about this time and coming up with the following problem. There were probably 150 participants. We convened as a group in the morning and would then split up into breakout sessions of about 6 people. The break sessions were assigned not chosen, and organizers tried to have as little overlap as possible, giving you the opportunity to meet the most number of people. So here is the question, what is the maximum number of breakout sessions until at least two people find themselves in a group again? After you figure that out, what is the maximum number of non-overlapping breakout session of size p chosen from an overall group size of n?

pic by lululemonathletica

Friday, June 12, 2009

Google's Formula

The cover of Wired's June issue has a three set Venn-Diagram. It looks nice even if it's logical relation to the main three stories are fluff. What I found exciting in the issue was the break out on the innovative way in which Google sells off advertising. Here is my attempt to condense this. For any given set of keywords, let's say like 'math', google holds an auction. All interested parties submit bids to have their add posted when someone searches for math. Who gets the first add on the search page? The highest bidder? No. Google has a quality ranking for each different add based on a number of factors. Google's idea is to keep the add material valuable to users. This is how they do it. They scale each advertiser's bid by the usefulness of the advertiser's add for someone who is searching for 'math'. How they get that quality score for each add involves a lot of data and a few company secrets. What does Google charge the companies for the adds? Not what the company bids. Instead they use the bid of the next highest ranking add, and they multiply it by the ratio of the quality scores of the two adds. The idea being that if your add is a better quality add than the second place bid, you pay proportionally less than their original bid. If it is worse, then you pay more. One interesting effect is that the 1st place add on any search page hasn't necessarily payed the most. If my description isn't working for you, check out pag 112 of the June issue of Wired. Like I said they have a really nice breakout explaining it, complete with an example.

Thursday, June 11, 2009

Cover Math Graphic

I liked this cover illustration from the June 2005 Harvard Business Review. 'It's something in his eyes?'

Wednesday, June 10, 2009

Geek of the Week How To

How can I become Geek of the Week? I get the question all the time. I have to admit. There is no formula. There is a lot of luck, and not a little bit of skill involved. For aspirants, MaximumPC has compiled a litmus test for basic geekdom. As they see it, there are 50 fundamental skills. Sue will be glad to know that the recitation of pi to at least 23 digits is on there. Check and see how many of these must have geek-skills you wield. You also might feel that they have overlooked some fundamentals. I'd love to hear what you would add in the comments.

pic by koolbadges

Tuesday, June 9, 2009

Lobachevsky Chair

I was at Housatonic Community College some weeks ago for a math conference. They have beautiful new facilities there, but most impressive are the chairs in the cafeteria. They kind of remind me of a hyperbolic plane. The geeky thing was that it was a math conference so I wasn't the only one noticing. Now I just need a set for my dining room.

Monday, June 8, 2009

Gruesome, but Fun

The following riddle about disabled veterans is from Lewis Carroll's A Tangled Tale.
Say that 70% have lost an eye, 75% an ear, 80% an arm, 85% a leg. What percentage, at least, must have lost all four?
Found this one in Herstein's Abstract Algebra. pic wikimedia

Friday, June 5, 2009

Math and Fragrance

I went to the mall last weekend with my wife, and was so excited to find an old friend there. She was locked away in glass (like all things of considerable value), but visible among the various other colognes. I couldn't wait to look up the cologne on Givenchy's website. Why did they call it pi? Will it make you smell like pi? Can you really smell like an irrational number? I was so dissappointed when I got home. Here is Givenchy's description of the fragrance.
PI is a fragrance dedicated to adventurers in search of new territories and sensational experiences. The Pi man is a man of action who always surpasses himself.
It's hard to glimpse even a metaphoric relationship between the number and the fragrance.

Thursday, June 4, 2009

Topology Question

Ken's mention of Menger Sponges brought up the association with the Cantor set and the Sierpinski triangle. There must be a name for a topological property of objects from which a congruent copy/s of itself can be removed and the remaining portions of the object are equivalent to the removed piece. The interval, cube, and triangle are all such objects. It seems to me that there is now way that the circle is. Togologists help!

Wednesday, June 3, 2009

Tuesday, June 2, 2009

781 dots

This image from the British Library is stunning. Found it on Flickr by sunny-drunk

Monday, June 1, 2009

Alfie's Children

This is one of my all time favorite problems to give to students.
Determine the ages of Alfie's children from analyzing the following conversation.

Alfie: Can you guess the age's of my children? The product of their ages is 36.

Bernice: That's not enough information.

Alfie: The sum of their ages is the same as our street address.

Bernice: I'll need a little more info.

Alfie: My oldest is a girl.

Bernice: Okay, I've got it.

pic by Alain Gree