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

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.

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!

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!

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.)

Mathematical Fortune

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

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