Tuesday, October 12, 2010
Thanks to Hebrew Academy of the Capital District ...
... for hosting students from schools all over the Capital District at our October 2010 Middle School Math Meet!
Names and scores of high-scoring students and the value-added whole-is-more-than-the-sum-of-the-parts team award will be posted in this space later this week after the administration window ends.
Thanks to George Reuter and Mike Curry of MathMeets.com for writing a great set of problems for our students! Thanks to student coaches Matthew Babbitt and Zubin Mukerjee as well as Albany Area Math Circle advisors Bill Babbitt and Rita Biswas for helping make the meet great. A special thanks to Albany Are Math Circle Advisor and Hebrew Academy math teacher Alexandra Schmidt for all the arrangements she made for us.
Would YOUR school like to host our next monthly math meet, scheduled for Sunday November 7? If so, please get in touch with us by sending an email to firstname.lastname@example.org.
In addition to working on those Math Meet problems, we also talked about fractals and other fun mathematical topics today.
In honor of the recent 10/10/10 day, we talked about powers of ten, powers of two, and 42.
For example, we talked about how 101010 in binary is 32+8+2=42 in decimal, and of course how 42 is a delightfully special number.
(In addition to being the Answer to the Ultimate Question of Life, the Universe and Everything, we noted that 10!seconds = 42 days (exactly!) because
[10x9x8x7x6x5x4x3x2x1 seconds]÷[(24 hours/day)x(60 minutes/hour)x(60 seconds/minute)]=42 days.
We also introduced the concept of "bimal" notation, which is the binary analog of decimal notation.
In bimal, 1/2 = 0.1, 1/4 = 0.01, 1/8 = 0.001, 1/16 = 0.00001, and so on.
This allows us to nicely express the following question:
What is 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + .... (and so on forever)?
In bimal, the answer is 0.111111111111111..... (and so on forever).
But, just as in decimal, 0.999999999...... = 1, in bimal 0.111111111.... = 1.
And we talked about a special kind of fractals, Pythagoras trees. In honor of Dr. Benoît Mandelbrot, who died a few days after our middle school math meet, I have moved our discussion of that topic to a separate post, Maverick Mathematicians and the Power of Grade School Geometry.