We proved that Pi is irrational!!

The highlight of today was in our two hour history of mathematics seminar when at the end it culminated in our proof that Pi is irrefutibly an irrational number!

Irrational, but well-rounded

We had to learn about how to work with continuous fractions and then do the proof by contradicting the definition of a rational number. We also proved that the number "e" is also irrational.

I've really enjoyed sleeping in the same bed for the past five nights, here is my home away from home this week.

Lamont Hall, Phillips Exeter Academy

Ok, now for a bit of Ernie Chen weirdness. This story starts with the fact that our seminars take place in the new Phelps Science Center here on campus. You all know that I have the world's smallest bladder so I see the inside of many bathrooms. So, here is what I saw. I figured out two of the patterns, can anyone help me out with the other two? Remember, these are the tile patterns in a science building.

Ground Floor

Main Floor

Second Floor

Third Floor

Ok, people, email me at echensf@hotmail.com with your guesses.

Rants and raves

1) Drivers in New Hampshire ACTUALLY follow the speed limit. What's the deal with that?
2) The pool here is awesome. I've been swimming every afternoon.
3) Exeter is one of the premiere prep schools in the nation and they have NO WIRELESS internet. Grumble....
4) Exeter is completely a PC campus. LOSERS.
5) The PC's they have don't have CD burners. Sheesh.
6) The weather has been perfect. 70's and no humidity. It rained once, while we were all sleeping.
7) There is another conference on campus as well. English teachers. They are much better looking and groomed.
8) The tech people have blocked all chatting software. TYRANTS.
9) I'm a quarter of the way through my trip. It's been great so far, let's hope it continues.

So you want to know about what I'm learning?

Each participant here takes two seminars. There are, however, three seminar periods in a day and I lucked out and have the first seminar period (8-10AM) free. So, Ernie Chen is sleeping in. There are, however, one hour talks that happen throughout the day and I have attended a couple of those.

At 10:30AM-12:30PM, I am in a seminar learning ways to use simulations in Statistics to make it more accessible to students. It is turning out that you can basically design an entire Statistics course around M&M's. Chi-squared is obvious, but one can aolso simulate an exponential regression by shaking a bunch of M&M's up and then removing those that aren't showing M's. We are also being exposed to the power of "Fathom", which is an amazing statistical software package. Today, I actually was able to understand the Central Limit Theorem for the first time. Let's just say that last year when I taught it, I was not exactly in complete command of the idea.

From 1:30PM-3:30PM, I am in a course touching some of the history of Math. This is the HEIGHT of geekdom. There are 13 of us in the class, but it's myself and three others that are totally grooving with the instructor. It's like our own personal seminar. Do I feel bad that the other's aren't keeping up? NO!!!!!!! I'm having way too much fun.

We started with the Babylonians and their numbering system. We moved onto Thales, the father of modern Geometry, and tackled the problem of quadrature of a polygon. Chris Davies if you are reading this, because we teach this, I totally rocked this in class. I had to shut myself up so I wouldn't look like a smartass. We then talked about the 3 problems that were unsolvable by classical mathematical antiquity.

1) Quadrature of a Circle
2) Trisecting and arbitrary angle
3) Doubling the volume of a cube

Well, with a bit of modern technology, we can create the following

The Cissoid

which allowed us to solve #3. And,

The Conchoid

which allowed us to solve #2. For those of you who want to see the proof, I'll show you.

Today, we worked with Archimedes and his method for deriving the formula for the volume of a sphere, using the concept of Moments. We also derived a way to find every single pythagorean triple using the rational points on a unit circle. (Davies, I have cool stuff for you).

Yeah, yeah, I drone on, but having the geektime of my life.

Zooperstars

The conference gives us a night off from Math and a group of about 35 of us took the option of getting on a bus and travelling an hour north on I-95 and going to Portland, ME to watch the Portland Sea Dogs (AA affiliate of the Boston Red Sox) take on the Norwich Navigators (AA affiliate of the San Francisco Giants). The game had its moments, but the highlight for all of us who attended was the in between inning entertainment. I have come to realize that minor league baseball games are hidden gems of American entertainment. For $7 the baseball was good, but watching things such as two men try to catch plastic lobsters in tandem in a lobster pot with the lobsters being hurled from 30 feet away with lacrosse sticks was nearly the height of low brow entertainment. There was another contest in which two kids were trying to get as many cans from one barrel to another. We watched a young girl, not as fast a runner as the boy against whom she was competing, get more cans across by using the ingenuity of dumping the cans into her shirt and carrying twice as many cans at a time as the boy did in his hands. The women of our group as well as the women in the stands were chanting girl power by the end. It was not a great time to be a male.

The HIGHLIGHT, however, was the special appearance of the Zooperstars.. Between the first and second inning is when it all began. I'll let my pictures tell you the entire story.

"Ichiroach Suzuki" dancing with "Harry Canary"

"Shark McGwire" in a danceoff with a Norwich Navigator player.

Navigator player gets it ON!

"Shark's" turn.

They aren't hugging in good sportsmanship here.

"Ichiroach" tangoing with "Tiger Woodchuck"

But the best was the following, hands down.

"Roger Clamens" chases down and swallows up a little kid.

"Clamens" spits up unedible parts of little boy.

I have to report that the hometown Sea Dogs lost to the Navigators 6-2 to remain in last place in the Eastern League's Northern Division. I implore anyone who has a chance to see the Zooperstars to make a special journey to whatever location they are playing. I'm still laughing at the hijinx!

Math Club

I am now at the Anja S. Greer Conference on Mathematics, Science and Technology. I will be here through Friday morning July 2nd. I am taking a course on teaching Statistics using simulations and hands-on projects and also a course on the History of Mathematics. MATH CLUB!

I have run into a couple of my former colleagues from The Lawrenceville School. It is great to see Nancy Thomas and Miranda Christofferson (sp?). John Jamison, from my Lakeside years, is also here teaching a seminar.

Off to geekdom..........

A weekend in Vermont

Friday evening, after dinner with Andy and his kids in Albany, I got into the car and drove east, across the bottom part of Vermont and up the Connecticut River (I-91) to visit my dear friend (and high school advisor) Anne S. and her husband David).

By the way, I finished White Teeth somewhere in Ohio and although I did enjoy the book was ultimately very disappointed by the ending. If anyone would like to discuss it, let me know. My current book on tape is the new David Sedaris book. It is quite funny, but I wish there were more stories about his living in Paris and stories about him and Hugh, his partner. I've had enough about his family.

Here's a montage of my weekend in Vermont.

 

 

 

 

Stephens Home (with my grandma rental car blocking the view)

The porch on which we sat and chatted for hours

The view from the porch

View from rear of the house

We did a great deal of catching up, talking about politics (mostly debating whether or not to see Fahrenheit 911 and we both we not see it), the Zantop killings and reading. One treat was that a friend of mine from Seattle (and also a friend of Anne and Dave's) came up from southern Vermont to have lunch with us on Saturday afternoon. Jenny K. and I worked together for a summer in Seattle and also attended the Klingenstein program for teachers in the summer of 1997. She worked for many years at Lakeside but now teaches at The Putney School, in Putney, VT. In the time since I have seen her last, she got married to Randy S. and is now three months pregnant with her first child. After lunch, we all took a walk. Probably some of the first exercise I have done in days.

Randy, Anne, Dave, Kayla (the Smith's dog) and Jenny

In addition, on Saturday night, we all went to a going away party for the farm manager of The Mountain School (the school Anne headed for many years) who is going on sabbatical. I met up with many people I know from the school and it was the first time many of them had seen me since my accident.

I try to make it up to Vermont to have some peace and quiet every year. I always am sad to leave.

I once did some questionable things with this guy....

After Cooperstown, I drove an hour and a half east to a suburb of Albany called Niskayuna, NY. I met up with a friend of mine from college who I had not seen since probably 1994. Andy V., a fellow Geology major, and I spent many hours in Snee Hall on the Cornell University campus. We probably spent more hours in bars and out in the great outdoors doing geological field work, but also just sitting around doing nothing and other things.

I'm pretty much a straight arrow and was in college too. Andy was one of the people who got me to do things I never would have done. Now look at him..........

Emma(4), Jack(10 months), Andy and Anna(6) V. (wife Johna not pictured)

I guess I find it amazing how great a father Andy is. I mean if these children ever want to know what their father was like in college, they should come and find me and he'll have to pay me off to not tell stories. Andy is now the father of three. When I knew Andy in college, he was living with a bunch of guys in a rundown apartment on Eddy Street in Ithaca and now he lives on a tree lined street near a country club in suburban Albany. How far he has come. I guess if I think about it, so have I, eh? I'm still shaking my head at the thought. But I'm am also sitting here thinking how WONDERFUL it is to see people that we have in our lives morph into new people (and better). Andy works as a project manager for an environmental consulting firm in the Albany area and is actually using the Geology training that he got in his career.

ANOTHER OBSERVATION
Mike and Michelle have just had their first child. Andy and Johna are on their third. It is QUITE amazing, and ultimately funny, the difference in which they handle their newborn children. With Mike and Michelle, everything is sterilized, every moment is caught on camera. Food is specially prepared and probably organic. There is a strict schedule and everyone has their duty. The baby is the focus of almost every moment of their lives. In contrast, Jack (Andy's 10 month old) is simply another child. Baby cries? Oh, wait a couple minutes and see if he shuts up. Sterilize bottles? Are you kidding? Diaper need changing? Do it right on the floor. Food? Pick a jar out of the pantry and get to it. Andy's girls are 4 and 6, and their baby brother is like a toy. Jack gets no special treatment. Mike and Michelle, this is what is going to happen to you when you get around to having #3 or #4......

Cooperstown, NY

After visiting Mike and Michelle in Ithaca, NY, I drove east on Friday June 25th and stopped in at the Baseball Hall of Fame in Cooperstown, NY. The museum itself is actually rather small and the displays are somewhat overwhelming in terms of the density of items per square inch. I love the fact that they have displayed the items in a chronological order and that the pathway of the museum is linear (meaning you follow one path and don't have to go back and forth between different displays, yes this is the mathematician in me), but just having so many things to try to look at in a case was too much for me.

For those of you who have never been to the hall, the first floor has a hall in which the plaque of each member of the hall is placed on the wall. It is said that .1% of all players who have made it into the major leagues actually get elected to the hall of fame. This year only two players are to be inducted, Dennis Eckersley and Paul Molitor. Two, that's it two.

In this main hall are statues of two of the greatest old school players, the Babe and Ted Williams. At first look, you have no idea that these statues are carved completely from a block of wood. Totally amazing.

The Babe

On the second floor, the displays are about great players, eras and "dynasties" during the history of major league play. One of my favorite players (although not a hall member, yet) is John Olerud. Olerud started his career with the Toronto Blue Jays and subsequently played for the New York Mets and now plays for my beloved (but at this moment horrendous) Seattle Mariners. Olerud is in the hall as part of the Toronto early 90's teams that for the first time ever, took the World Series trophy north of the border.

A young John Olerud

The third floor of the hall concentrates on the different records and the history of the world series. For $8.50 (with a AAA discount) it was definately a great way to spend and afternoon.