Math Circle in March and Pi Day

Two weeks ago we examined how Zorgons count.  Unlike us with 10 digits on our hands, the Zorgons have no fingers, which means they count in binary.   A lot of what I used was based on a lesson by Rick Garlikov. We learned how to count up to the number 32 in binary (or Zorgon) and learned a deeper understanding of columns and place value.  I hope this helps them in understanding our own base 10 system.  Eventually, I hope to bring our discussion of binary numbers back to the Game of Nim.   After working through the basics of Garlikov’s inquiry, I moved onto some ideas from Math Maniacs.   The students practiced generating binary numbers using a set of flashcards and tried generating numbers up to 32.

This past week was a double treat for Math Circle.  On Wednesday, Pi Day, the student measured the circumference and diameter of several objects around the classroom and found the ratio between them.  Maura explains in detail on the main Melrose Math Circle site our lesson from that day.  We finished with a quick exploration of Buffon’s Needle.  This is a need example using a Monte Carlo simulation which the students watched to estimate Pi.  The basic idea is that if you drop needles there is a relationship between the number of drops and how many times the needles will happen to cross a set of parallel lines which comes up with an estimate of Pi.

As an aside I was reading about how to generate Pi in binary.  Turns out, it is a bit easier to remember in binary.  I found this great binary web-site that has some stuff a bit more advanced.   Lots of students learn binary counting, but I had never learned binary floating point numbers before.  But it makes sense that instead of 0.1 being 1/10th it would be 1/2 in binary.  Working this way

Pi = 11.001001000011111

which is actually easier to remember that 3.1415926535897932384

On Thursday, at the CEEO we had our first Staff Math Circle.  We explored an interesting nine digit problem.  The problem is how can you arrange nine digits in such a way that the first digit is divisible by one, the second by two, the third by three, etc.  This problem relies on a lot of elementary school mathematics, but was challenging enough that it took us the entire hour to work through the problem.  We had a few undergraduates working on LEGO NXT Robot projects who were quick to jump to the answers. Perhaps they had a fresher memory of 6th grade mathematics!

This Wednesday we will return to binary counting and will venture into binary arithmetic.