Sunday, April 24, 2016

Some short bits from the Gathering for Gardner Conference

I attended G4G12 (Gathering for Gardner) a conference that meets every 2 years (though the gap between the first and second was three years) to celebrate the work of Martin Gardner. Most of the talks were on Recreational mathematics, but there were also some on Magic and some are hard to classify.

Martin Gardner had a column in Scientific American called Mathematical Games from 1956 to 1981. His column inspired man people to go into mathematics. Or perhaps people who liked math read his column. The first theorem I ever read outside of a classroom was in his column. It was, in our terminology, a graph is Eulerian iff every vertex has even degree.

For a joint review of six G4G proceedings see here. For a joint review of six books on recreational math including three of Gardner's, see here. For a review of a book that has serious math based on the math he presented in his column see here.

The talks at G4G are usually 6 minutes long so you can learn about a nice problem and then work on it yourself. Their were a large variety of talks and topics. Many of the talks do not have an accompanying paper. Many of them are not on original material. But none of this matters--- the talks were largely interesting and told me stuff I didn't know.

64=64 and Fibonacci, as Studied by Lewis Caroll, by Stuart Moshowitz. This was about a Lewis Caroll puzzle where he put together shapes in one way to get a rectangle of area 65, and another way to get a square of area 64, The following link is NOT to his talk or a paper of Moshowitz, but it is about the problem: here

How Math can Save your life by Susan Marie Frontczak. This was part talk about bricks and weights and then she stood on the desk and sang this song (thats not her signing it).

Twelve ways to trisect and angle by David Richeson. This was NOT a talk about cranks who thought they had trisected and angle with straightedge and compass. It was about people who used ruler, compass, and JUST ONE MORE THING. I asked David later if the people who trisected the angle before it was shown impossible had a research plan to remove the ONE MORE THING and get the real trisection. He said no- people pretty much knew it was impossible even before the proof.

The Sleeping Beauty Paradox Resolved by Pradeep Mutalik. This paradox would take an entire blog post to explains so here is a pointer to the wikipedia entry on it: here. AH, this one DOES have a paper associated to it, so you can read his resolution here

Larger Golomb Rulers by Tomas Rokicki. A Golomb Ruler is a ruler with marks on it so that the all of the distances between marks are distinct. The number of marks is called the order of the ruler. Construction a Golumb ruler is easy (e.g., marks at the 1,2,4,8,... positions I think works). The real question is to get one of shortest length. They had some new results but, alas, I can't find them on the web.

Chemical Pi by John Conway.  There are people who memorize the first x digits of pi. John Conway does something else. He has memorized the digits of pi and the chemical elements in the following way:

HYDROGEN  3.141592653 HELIUM next 10 digits of pi LITHIUM etc

that is, he memorized the digits of pi by groups of 10 and separated by the chemical elements in the order they are on the Periodic table. He claims this makes it easier to answer questions like: What is the 87th digits of pi. He also claims it gives a natural stopping point for how many digits of pi you need to memorize (need? maybe want). (ADDED LATER WHEN I CORRECTED HELIUM TO HYDROGEN: here are some mnemonic devices:  here.

This post is getting long so I may report on more of the talks in a later post.