Pascal's triangle in sidewalk chalk

First 15 rows of Pascal's triangle (mod 2) in sidewalk chalk

Imagine that you throw a dart at Pascal's triangle.  What are the odds you will hit an even number?

Paul Zeitz raised this fascinating question at the MSRI Great Circle's workshop three years ago.

It's a fun one to explore in sidewalk chalk--perfect for Guerrilla Math Circles.

A good way to start thinking about this problem is simply to begin coloring in the triangle--and what could be more fun that the idea of creating a really large one with sidewalk chalk?  And engaging any curious passersby in helping you.  How big can we make it if we get lots of folks helping us?  (And of course, we could also start some people on exploring Pascal's triangles with multiples of other prime numbers colored in.)

I started one the other day in Schenectady's Central Park and I will be back there this evening (Friday June 8) to do more.  There is a nice large stretch of blacktop that is blocked off from automobile access.  It is adjacent to Tiny Totland and not far from the Music Haven (site of many wonderful free concerts) and also near the picnic pavillion area where Schenectady Inner City Mission serves free lunches in the summer.  Central Park is the "crown jewel" of Schenectady's park system, designed by Frederick Olmsted and with a world class rose garden.  To get to where I will be tonight, enter Central Park via the main entrance off Central Parkway and then turn to the left when you get to the lake.  Park in the parking lot near Tiny Totland and look for me in the blacktop area between Tiny Totland and the lake.

On Sunday afternoon, from 1 to 5 p.m. I will be doing more Guerrilla Math Circles at a different park in Schenectady, Jerry Burrell Park.  Jerry Burrell Park is a place that is near and dear to my heart, because one of my former students at Union College, Jeremy Taglieri, spent a year working along with two friends to raise $84,000 in funds and recruiting 140 volunteers to renovate the park.  They called their project Project SKIP, where SKIP = "Schenectady Kids Imagine and Play."  Jerry Burrell Park is also the site of a SICM free lunch site, and in fact, volunteers from my own church will take a turn serving lunch for a week there later this summer.

I invite Albany Area Math Circle families (students, parents, siblings) to join me in sharing the fun, beauty, and awesomeness of mathematics with a wider world, a world of folks who have yet to discover how much delight can be had in exploring the wilds of mathematics.

All of you can do these activities wherever your parents feel comfortable with your doing them.  I grew up in a city myself, and have always been comfortable having my children play in Schenectady parks when they were growing up, with--of course--sensible precautions taken about when and where to go.  Personally, I am comfortable being in city parks when SICM volunteers from churches all over the area are serving free lunches, but not when they are mostly deserted.  And this Sunday's event at Jerry Burrell Park is part of a larger event organized by city officials.

Nothing is ever 100% safe--and there are risks to just sitting in your own living room (a car might come crashing through the wall), but I recognize that these are decisions that math circle parents needs to make for their own children.  I feel compelled to point out that--sadly--just a few weeks after the renovation of the Jerry Burrell Park in 2010, a 17-year-old boy shot and seriously wounded an 11-year-old and an 18-year-old boy who were walking to the park from just a block away.

But--remember that you and your sons and daughters can also do these same activities WHEREVER you happen to be--on the sidewalk in front of your own home or the park just down the street from you in your own neighborhood.

No matter where you are comfortable with participating in our outreach activities, you can work with us to brainstorm ideas and post links to photos in the comments below.  Albany Area Math Circle members can also post about their experiences in our private discussion forum on the Art of Problem Solving.