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May Problem and Solution!!!

Hey Guys! In May of 2011 the Bard Math Circle visited the Kingston Library and challenged the enthusiastic students to solve a series of combination/permutation problems. Although tough, the problems proved to be quite the adventure for the talented youth. One of the problems asked to find the different ways that four friends could split into two group (groups can be uneven) if they were to play a game. Here is the problem:

Four friends, Andrew, Brianna, Cassandra, and Darien want to
play a game. How many ways can they form two teams? Every-
one must play.
Example: Andrew, Cassandra, Darien vs. Brianna .
This is the same as Brianna vs. Darien, Andrew, Cassandra

Actually, this is a similar situation to my 2011 Summer at Bard College adventures with three friends of mine (Anam, Andres, Mauricio). We were having a dance competition and we could either partner up in a group or give a solo performance. We first gave everyone the chance to prove themselves the best dancer. This gave us four groups. Next, Anam got a partner. She had three dances with a partner. Then, Andres had the chance to get a partner as well and he danced only twice (he had already danced with Anam). Later, Mauricio had to get a partner and he only danced with me (he had already danced with Andres and Anam). When it was my turn, I realized I had already danced with all of them and I was too tired of dancing. Nonetheless, it was a fun night and full of laughs, combinations, and math.

It turns out the number of groups we could create was 7. We could abbreviate Andrew as A, Brianna as B, Cassandra as C, and Darien as D. Then the example Andrew, Cassandra, Darien vs. Brianna could be written as ACD|B. To make things easy, let’s agree to always list Andrew’s team first:

  1. A|BCD
  2. AB|CD
  3. AC|BD
  4. AD|BC
  5. ABC|D
  6. ABD|C
  7. ACD|B
For further information on combination and permutation problems, the following website can help http://www.mathsisfun.com/combinatorics/combinations-permutations.html

If you are looking for more practice the following is very helpful http://www.regentsprep.org/Regents/math/algtrig/ATS5/PCPrac.htm

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Yesterday my children and I attended the Math Circle at Kingston Library.  On the way home I asked them each what their favorite part of the Math Circle was.  Jordan said ” When I beat Jeannette at 21 Nim!” followed by her trademark giggle.   Michael enjoyed the time the Xingye spent with him explaining square roots and especially liked that Xingye signed his cast in Chinese.  Alisa liked playing with the magnetic shapes.  I loved all the energy in the room and seeing parents and children having fun using their math skills!

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Math Circle at Exploration School

Exploration School is a summer enrichment program housed at the campuses of St. Mark’s School (Junior– grades 4-7), Wellesley College (Intermediate– grades 8-9), and Yale University (Senior– grades 10-12). This summer I had the opportunity to work as an instructor at the Intermediate Program. My ingredients were students with a love of learning, a room to put them, and a bunch of math games and puzzles– my result was Math Circle! 

The Math Circle at Explo happened 3 times– each time, there were more kids excited to play SET, solve Rubix cubes, and work on problems. Some students attended in order to try the games, and some students wanted to practice algebra, trigonometry, or even calculus!
An important concept at Exploration School is legacy– there is an overarching goal to create a safe, unique and exciting space that eager students can come back to summer after summer. Perhaps Math Circle will become a legacy!
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Here’s a picture of Nathaniel from our first Math Circle session at Sarah Hull Hallock Library in Milton yesterday. What do you think of his origami creations?

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Added: static pages

I just added our first static page! Normally, posts cycle out and you have to find them in the archives, but not so with a static page. Blogger allows up to 10 static pages, and the first one I added is “Calendar”.

It’s easy to do: from the Posting tab, just choose “Edit Pages”. It’s pretty clear from there.

Here’s a webpage that walks you through it as well: blogger-static-pages

The question now is, what static pages should we add? Please comment on this post with your suggestions for static pages.

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Writing Mathematics on our Blog with Texify!

I just learned today from Mary O’Keeffe how to include mathematics on blogger. It’s not native, but does the trick, and especially a little useful if you know a little LaTeX, the mathematical typesetting language.

Let’s say you want to typset the quadratic formula. In LaTeX, you would write this as

$\frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$

Now just visit the texify web site: Texify and insert the LaTeX code where specified. The Texify website will then automatically generate html code for your formula, resulting in:

\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
It works pretty well. If I had a blogger wish, it would be for LaTeX to be recognized natively!
For those who don’t know, Mary O’Keeffe directs the Albany Area Math Circle and is also co-director for the Math Prize for Girls. She’s a great resource for math circles around the country, and seeing as our math circles are so close together, I’ve hoped for several years that we’ll find ways to coordinate some math circle activities. One idea – let’s visit the Museum of Mathematics together when they open in 2012!
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Set

I think that SET is my favorite Math Circle game. Not only is it challenging and fast-paced, but it has a great community aspect to it: players can join in during the middle of the game, or choose to play for a few minutes. A friend of mine found a SET app on her phone the other day, so we were playing while at a local Open-Mic night. A second friend saw it, played with us until she found a SET, and then returned to her group. It’s that fast, and that fun.

Another way to play SET is to visit this website. There are 12 cards on the table and 6 SETs that you must find; every day there is a new puzzle. How long does it take you to find them all? My record is 42 seconds–can you beat that?

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Calendar Added

I just added the Bard Math Circle calendar to this blog. It’s in the right column, in agenda form. I added a gadget, and searched for one that adds a calendar. Easier than I thought it would be!

This means that we should start populating the calendar with Fall semester events.

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The Bard Math Circle Logo

We now have a logo! Featured on the right side of this page, you’ll see a version of the Fibonacci Spiral, designed by artist David Levine. The Fibonacci Spiral consists of squares, each with a 90 degree arc, arranged in a spiral form. The dimensions of the rectangle are consecutive Fibonacci numbers, and thus approximate the Golden Ratio.

We’re looking forward to featuring this logo on all Bard Math Circle materials!