• The nautilus shell is not a real-world example of the golden ratio, even though we've been told countless times that it is. ('We' would be anyone who reads much popular math exposition.) An email correspondent (here's his blog) pointed me to gowers, whose post on a book he compiled pointed me to the fascinating God Plays Dice blog, which pointed me to the Shallow Thoughts blog, in which Akanna Peck documents the mismatch of shells and golden ratio spiral. (I'd say the thoughts are anything but shallow. Her reference is to shallow sky, which is the solar system.)
• How to model a hand! Maria Droujkova's natural math google group included a discussion titled Changing Shapes with Matrices that pointed me to this youtube video on modeling a hand in 3D. My son and I also liked this one on modeling a head.
And then, of course, I learned more about tools out there on the Web. I signed up for twitter, even though I won't use it on a cell phone, so that I could read Maria D's notes on the Great Circles conference. And as much as I try to follow Maria's work, it took another site to point me to this slide show of hers about all the sorts of math-related social sites kids might want to participate in.
Great Circles Conference at MSRI
With help from Maria's notes, here are some of the cool things those math circle folks are doing:
• Mary O'Keeffe, who founded the Albany Area Math Circle, spoke with passion about how she includes kids at different levels.
• Bob & Ellen Kaplan, from the Boston area, did math circles with younger kids. Their 'always collegial, never competitive' vision of math circles will be an important part of the anthology I'm putting together. (Their website is here.) I have already used Ellen's pancake problem (what is the greatest number of pieces we can get with n cuts through a circle?) with my Wildcat kids and some college students.
• Janet Metz's talk on Gender, Culture, and Math was riveting. She used the infamous remarks made by Larry Summers (formerly pres of Harvard, now economic advisor to Obama) that questioned women's ability to excel in math and the sciences, as a springboard for introducing some great statistical evidence to the contrary. Here's a paper she co-authored on this.
Summers imagined that men and women have the same average intelligence, but that men's varies more (more men are either kinda dumb or exceedingly smart), and imagined that this, along with women stopping to have babies, was why Harvard has no tenured women in math. (Here's a Slate article for more background.) I say imagined because the evidence is clear that the 3rd reason he gave, and then basically dismissed, namely discrimination, is clearly the dominant force. If you look at international data, for instance this page from World Economic Forum, you see that performance on math tests is closely linked to the Gender Gap Index. Of note is girls' performance in Iceland, where they do better in math than the boys do.
• Fred Smyth, of the Full Potential Initiative, gave another riveting talk on the psychological dimensions of women's under-representation in mathematics, titled Implicit Attitudes and Stereotypes matter in Math and Science.
• Tom Davis gave a great talk about using math to think about geography. His website is here.
• Zvezdelina Stankova talked about some of the stories in her new book, A Decade of the Berkeley Math Circle.
I'll edit this post as soon as I can find out who said this, but I can't leave it out. One of the programs described got kids analyzing art mathematically, and a bunch of them were standing in a museum discussing a piece. An adult walked up and asked what they were talking about, and... "Suddenly this kid, who was a failure in math, was talking to adults about topology in statues."