Thursday, December 31, 2009

excellent new issue of Girls Angle bulletin

The bulletin is put together by the Girls Angle program in Cambridge, MA, where the mentors include Harvard and MIT students and faculty working with girls in grades 5 through 11. The bulletin is chock full of delights for the younger members of Albany Area Math Circle, for our older students looking for ideas to mentor them, and for all those who are young at heart mathematically, no matter what their gender.

Check their latest issue out here!

Harvard freshman Amy Tai has written a beautiful and very engaging exposition of the properties of the medians of a triangle, which begins on page 2.

Hah! I can see some eyelids drooping already.

The medians of a triangle....how exciting a topic could that be? Like watching paint dry, some of you are probably thinking to yourselves.

Too many American high school students think of geometry as a dull subject to be gulped down like cod-liver oil before moving on to more advanced topics. Amy's article makes the topic come alive as she invites the reader into the exploration along with her.

Amy's article is a superb model for younger students who really want to develop their geometric intuition AND learn how to write crystal-clear mathematical expository prose. Her illustrations make a potentially dull topic spring to life in a memorable way.

Our Albany Area Math Circle high school students who are mentoring younger students can gain some very valuable insights and ideas from reading Amy's article and related pieces in the bulletin.

The Girls' Angle bulletin also contains more articles that generalize on the idea of the median. A median of a triangle is a line passing through a vertex that cuts the area of the triangle in half. Determining the analogs for more complicated polygons turns out to be a very fascinating activity. Try finding those lines for the shapes on page 15. They start out easy, and then require more and more ingenuity as you move down the page. They are sort of like potato chips--bet you can't eat just one!

The latest Girls Angle bulletin also features a story written by MIT senior Maria Monks about the adventures of a young mathematician named Emmy Newton. Maria writes in a way that invites the reader to solve the puzzle along with--or even before--Emmy does. Congratulations to Maria, who has won many honors, including Honorable Mention for the 2010 AMS/MAA/SIAM Morgan Prize for outstanding research in mathematics by an undergraduate. She will be giving a talk on her research at the Joint Math Meetings in San Francisco next month.

Who can resist the mathematical treasure hunts included in the pages of this issue? If you think you can solve the one on page 10, you are invited to send your solution into the journal. You could, of course, take the easy way out and use a calculator to solve it, but students may discover many beautiful ideas if they take their time and think through the problem in a different way. Our middle school math circle students who heard me talk about bimal last fall may especially enjoy thinking through a part of the problem that intially looks long and computationally messy--but it isn't really, once you think about the meaning of bimal(bimal is the binary analog of decimal notation.)

Kudos to the creators of this excellent bulletin. There's much more packed in the issue that looks fascinating and promising as well. Back issues are also available on-line in their archive here. There are many more treasures there.