Math News

Fast Base Running

In baseball, what’s the fastest way around the bases?

If you hit a long ball and know you can reach at least second base, then rather run in a straight line towards first base, you should veer towards the dugout in a circular fashion. The optimal baserunning path is one that is studied by Williams College math professor Frank Morgan. He claims that by cutting off the corners, an average runner can reach the home plate 4 seconds earlier!

baseball base running

In the above picture, home plate is the bottom dot and going counterclockwise we have 1st, 2nd and 3rd base. If you watch baseball, you’ll see that most of the time the players run in a straight line towards first, even if they hit a long ball.

How To Beat Traffic Mathematically

Brandon Hansen has an interesting article about traffic where he analyzes data that he recorded for a period of a year. He kept track of his departure and arrival times both to and from work. After a detailed analysis, he concludes that he can save over 30 hours per year by simply moving his schedule out a half-hour!!

traffic diagram

Perhaps one day our cars will be able to track and analyze traffic data for us automatically and tell us when the best time to leave the house is.

What shape dice pack tighter than any other shape?

tetrahedral dice
tetrahedral dice
tetrahedral dice
tetrahedral dice

Last year, physicists Jaoshvili, Esakia, Porrati and Chaikin published a paper in Physical Review Letters confirming that the D4-shaped tetrahedral die pack more densely than any other shape (yet tested).

“The revelation is the result of a series of experiments that involved pouring tetrahedral dice into containers, shaking them, and adding more dice until the containers were completely filled. After adding water to measure the open space between the dice, the researchers confirmed that the tetrahedrons fill roughly 76% of the available space in a large container. Similar experiments with spheres typically only fill containers to about 64% of the total volume.”

Applications of the research include the flow of granular materials like sand and gravel, the storage of information in digital memory, and determining optimal shapes for packaging consumer products.

Who is XXX?

Back in 2005, the AMS published the following blurb:

“The MR Author Database contains many interesting names, for example pseudonyms, one of which is Tom Odda. Another is XXX, the author of one paper in the database.”

Proof of this as shown below:

“Do you have information about who XXX is? Send your documented answer to by September 1, 2005. Our author identification staff will assess the validity of the answers and choose a correct one–we don’t know the answer, or it would be in the database already. All correct answers will be entered into a drawing for a $25 AMS gift certificate. XXX him/herself is an automatic winner.”

Does anyone know if this was ever settled? Did the AMS publish something about this after 2005?

RIP: Mathematician John Selfridge

News has it that mathematician John L. Selfridge (born February 17, 1927) has passed away on Sunday, October 31st, 2010. Selfridge was an American mathematician who made contributions to the fields of analytic number theory, computational number theory, and combinatorics. His main collaborators were Paul Erdős (14 papers) and Richard Guy (10 papers).

He was executive editor of Mathematical Reviews from 1978 to 1986 and also a founder of the Number Theory Foundation.

Wikipedia Link
Genealogy Link

Fields medal 2010

The Fields Medals have been announced today. The four winners are:

  • Elon Lindenstrauss (for analytic work with applications to number theory)
  • Ngô Bảo Châu (for analytic work with applications to number theory)
  • Stanislav Smirnov (for theoretical work in statistical physics)
  • Cedric Villani (for theoretical work in statistical physics).

made far-reaching advances in ergodic theory (the study of statistical behavior of dynamical systems); Ngô gave a proof of a long-standing conjecture in number theory, namely, the Fundamental Lemma; Smirnov brought mathematical rigor to statistical physics; and Villani made deep connections between mathematics and physics, especially in the topic of entropy.

God’s number is 20

rubiks cube

A team of researchers has shown that no position of the Rubik’s cube requires more than 20 moves by using around 35 CPU-years of idle computer time donated by Google. The algorithms used by those fast cube solvers typically require more than 40 moves.

“One may suppose God would use a much more efficient algorithm, one that always uses the shortest sequence of moves; this is known as God’s Algorithm. The number of moves this algorithm would take in the worst case is called God’s Number. At long last, God’s Number has been shown to be 20.”

It should be noted that there exists configurations of the Rubik’s cube which require at least 20 moves to solve, as shown by Michael Reid who proved that the ”superflip” position requires 20 moves.